Shanks and methods for forming such shanks

ABSTRACT

A shank ( 110 ) comprises a captive portion ( 116 ) comprising a longitudinal central axis ( 112 ), a captive end ( 118 ), a first set ( 117 ) of first structures ( 120   a ), and a second set ( 119 ) of second structure ( 120   b ). The second set ( 119 ) of the second structures ( 120   b ) is closer to the captive end ( 118 ) than the first set ( 117 ) of the first structures ( 120   a ). The first set ( 117 ) of the first structures ( 120   a ) has a first axial compliance coefficient along the longitudinal central axis ( 112 ). The second set ( 119 ) of the second structures ( 120   b ) has a second axial compliance coefficient along the longitudinal central axis ( 112 ). The first axial compliance coefficient of the first set ( 117 ) of the first structures ( 120   a ) is greater than the second axial compliance coefficient of the second set ( 119 ) of the second structures ( 120   b ).

BACKGROUND

A machining cutter, such as an end mill or, more generally, a shank, hasa tendency to “walk out” of its receiver (or collet) when used for heavymachining operations during which large quantities of material aremachined away in a single pass. Such “walk-out” of the cutter leads to aloss of machining accuracy, thus significantly increasing manufacturingcosts. Conventional approaches to this problem are generally limited tothe use of bulkier receivers and/or slower linear speeds and/orshallower depths of cut. However, these approaches are associated withvarious disadvantages, such as reduced maneuverability of the machiningequipment as well as restricted access to the workpiece.

A “walk-out” phenomenon will now be briefly discussed without beingrestricted to any particular theory. Prior to introduction of lateralforces between a shank and a receiver during, e.g., a milling operation,an inside wall of the receiver contacts the shank circumferentially anduniformly, maintaining static friction between the shank and thereceiver and retaining the shank within the receiver. When lateralforces are introduced, the receiver may locally elastically deform,resulting in a loss of static friction between the shank and thereceiver. As a result, slippage of the shank relative to the receivermay occur.

SUMMARY

Accordingly, apparatuses and methods, intended to address at least theabove-identified concerns, would find utility.

The following is a non-exhaustive list of examples, which may or may notbe claimed, of the subject matter according the present disclosure.

One example of the present disclosure relates to a shank comprising acaptive portion comprising a longitudinal central axis. The shank alsocomprises a captive end, a first set of first structures, and a secondset of second structure. The first structures extend away from thelongitudinal central axis in a direction normal to the longitudinalcentral axis. The second structures extend away from the longitudinalcentral axis in a direction normal to the longitudinal central axis. Thefirst set of the first structures and the second set of the secondstructures are each half as long along the longitudinal central axis asthe captive portion. The first set of the first structures and thesecond set of the second structures do not overlap along thelongitudinal central axis. The second set of the second structures iscloser to the captive end than the first set of the first structures.The first set of the first structures has a first axial compliancecoefficient along the longitudinal central axis. The second set of thesecond structures has a second axial compliance coefficient along thelongitudinal central axis. The first axial compliance coefficient of thefirst set of the first structures is greater than the second axialcompliance coefficient of the second set of the second structures.

Another example of the present disclosure relates a shank comprising acaptive portion comprising a longitudinal central axis. The shank alsocomprises a captive end, a first set of first structures, and a secondset of second structures. The first structures extend away from thelongitudinal central axis in a direction normal to the longitudinalcentral axis. The second structures extend away from the longitudinalcentral axis in a direction normal to the longitudinal central axis. Thefirst set of the first structures and the second set of the secondstructures are indirectly connected together.

Yet another example of the present disclosure relates to a method offorming a shank. The method comprises arranging first structures in afirst set of the first structures and second structures in a second setof the second structures such that the first structures and the secondstructures extend away from a longitudinal central axis in a directionnormal to the longitudinal central axis. The method also comprisesindirectly bonding the first set of the first structures to the secondset of the second structures.

BRIEF DESCRIPTION OF THE DRAWINGS

Having thus described examples of the present disclosure in generalterms, reference will now be made to the accompanying drawings, whichare not necessarily drawn to scale, and wherein like referencecharacters designate the same or similar parts throughout the severalviews, and wherein:

FIG. 1 is a block diagram of a shank, according to one or more examplesof the present disclosure;

FIG. 2A is a schematic sectional view of a rotating receiver-and-shankassembly subjected to a lateral force;

FIGS. 2B is a schematic sectional view of the rotatingreceiver-and-shank assembly of FIG. 2A with the lateral force in a firstorientation relative to the assembly;

FIGS. 2C is a schematic sectional view of the rotatingreceiver-and-shank assembly of FIG. 2A with the lateral force in asecond orientation relative to the assembly;

FIGS. 3A is a schematic sectional view of a receiver-and-shank assembly,in which neither the receiver nor the shank has structural forincreasing axial compliance, prior to applying a lateral force to theshank;

FIGS. 3B-3D are schematic sectional views of the receiver-and-shankassembly of FIG. 3A, wherein the shank is subjected to a lateral forceapplied in two different orientations relative to the shank;

FIGS. 3E is a schematic sectional view of a shank having structures,according to one or more examples of the present disclosure, havingstructures engaging a receiver, prior to applying a lateral force to theshank,;

FIGS. 3F-3H are schematic sectional views of the shank of FIG. 3E,according to one or more examples of the present disclosure, having thestructures engaging the receiver, as shown in FIG. 3E, wherein the shankis subjected to a lateral force applied in two different orientationsrelative to the shank;

FIG. 4A is a schematic sectional view of a receiver-and-shank assemblythat is not deformed and/or subjected to a lateral force;

FIG. 4B is a schematic sectional view of a receiver-and-shank assemblyexhibiting a constant-angle deformation due to, for example, beingsubjected a lateral force;

FIG. 4C is a schematic sectional view of a receiver-and-shank assemblyexhibiting a variable-angle deformation, due to, for example, beingsubjected a lateral force;

FIGS. 5A-5B and 6A-6B are schematic sectional views of two portions ofthe receiver shown in FIG. 4C at two different angle deformations;

FIG. 7A is a schematic sectional view of the shank of FIG. 1, comprisingtwo structures having different widths, according to one or moreexamples of the present disclosure;

FIG. 7B is a schematic sectional view of the shank of FIG. 1, comprisingtwo structures having different camber angles, according to one or moreexamples of the present disclosure;

FIG. 7C is a schematic sectional view of the shank of FIG. 1, in whichthe first structures and the second structures have identical combinedlengths but different combined widths, according to one or more examplesof the present disclosure;

FIG. 7D is a schematic sectional view of the shank of FIG. 1, in whichthe first structures have a smaller combined length than the secondstructures, according to one or more examples of the present disclosure;

FIG. 7E is a schematic sectional view of the shank of FIG. 1, in whichthe first structures have a greater combined length than the secondstructures but in which the first structures and the second structureshave identical combined widths, according to one or more examples of thepresent disclosure;

FIG. 8A is a schematic sectional view of the shank of FIG. 1, accordingto one or more examples of the present disclosure, and a receiver priorto fitting the shank into the receiver;

FIG. 8B is a schematic sectional view of the shank shown in FIG. 8A,according to one or more examples of the present disclosure;

FIG. 9A is a schematic sectional view of structures of the shank of FIG.1, according to one or more examples of the present disclosure, prior toconnecting the structures;

FIG. 9B is a schematic sectional view of the shank of FIG. 1, accordingto one or more examples of the present disclosure, after connecting thestructures shown in FIG. 9A;

FIG. 10 is a block diagram of a method of forming the shank of FIG. 1,according to one or more examples of the present disclosure;

FIG. 11 is a block diagram of aircraft production and servicemethodology; and

FIG. 12 is a schematic illustration of an aircraft.

DETAILED DESCRIPTION

In FIG. 1, referred to above, solid lines, if any, connecting variouselements and/or components may represent mechanical, electrical, fluid,optical, electromagnetic and other couplings and/or combinationsthereof. As used herein, “coupled” means associated directly as well asindirectly. For example, a member A may be directly associated with amember B, or may be indirectly associated therewith, e.g., via anothermember C. It will be understood that not all relationships among thevarious disclosed elements are necessarily represented. Accordingly,couplings other than those depicted in the block diagrams may alsoexist. Dashed lines, if any, connecting blocks designating the variouselements and/or components represent couplings similar in function andpurpose to those represented by solid lines; however, couplingsrepresented by the dashed lines may either be selectively provided ormay relate to alternative examples of the present disclosure. Likewise,elements and/or components, if any, represented with dashed lines,indicate alternative examples of the present disclosure. One or moreelements shown in solid and/or dashed lines may be omitted from aparticular example without departing from the scope of the presentdisclosure. Environmental elements, if any, are represented with dottedlines. Virtual (imaginary) elements may also be shown for clarity. Thoseskilled in the art will appreciate that some of the features illustratedin FIG. 1 may be combined in various ways without the need to includeother features described in FIG. 1, other drawing figures, and/or theaccompanying disclosure, even though such combination or combinationsare not explicitly illustrated herein. Similarly, additional featuresnot limited to the examples presented, may be combined with some or allof the features shown and described herein.

In FIGS. 10 and 11, referred to above, the blocks may representoperations and/or portions thereof and lines connecting the variousblocks do not imply any particular order or dependency of the operationsor portions thereof. Blocks represented by dashed lines indicatealternative operations and/or portions thereof. Dashed lines, if any,connecting the various blocks represent alternative dependencies of theoperations or portions thereof. It will be understood that not alldependencies among the various disclosed operations are necessarilyrepresented. FIGS. 10 and 11 and the accompanying disclosure describingthe operations of the method(s) set forth herein should not beinterpreted as necessarily determining a sequence in which theoperations are to be performed. Rather, although one illustrative orderis indicated, it is to be understood that the sequence of the operationsmay be modified when appropriate. Accordingly, certain operations may beperformed in a different order or simultaneously. Additionally, thoseskilled in the art will appreciate that not all operations describedneed be performed.

In the following description, numerous specific details are set forth toprovide a thorough understanding of the disclosed concepts, which may bepracticed without some or all of these particulars. In other instances,details of known devices and/or processes have been omitted to avoidunnecessarily obscuring the disclosure. While some concepts will bedescribed in conjunction with specific examples, it will be understoodthat these examples are not intended to be limiting.

Unless otherwise indicated, the terms “first,” “second,” etc. are usedherein merely as labels, and are not intended to impose ordinal,positional, or hierarchical requirements on the items to which theseterms refer. Moreover, reference to, e.g., a “second” item does notrequire or preclude the existence of, e.g., a “first” or lower-numbereditem, and/or, e.g., a “third” or higher-numbered item.

Reference herein to “one example” means that one or more feature,structure, or characteristic described in connection with the example isincluded in at least one implementation. The phrase “one example” invarious places in the specification may or may not be referring to thesame example.

Illustrative, non-exhaustive examples, which may or may not be claimed,of the subject matter according the present disclosure are providedbelow.

Referring, e.g., to FIGS. 1, 8A, 8B, 9A, and 9B, shank 110 is disclosed.Shank 110 comprises captive portion 116 comprising longitudinal centralaxis 112. Shank 110 also comprises captive end 118, first set 117 offirst structures 120 a, and second set 119 of second structure 120 b.First structures 120 a extend away from longitudinal central axis 112 ina direction normal to longitudinal central axis 112. Second structures120 b extend away from longitudinal central axis 112 in a directionnormal to longitudinal central axis 112. First set 117 of firststructures 120 a and second set 119 of second structures 120 b are eachhalf as long along longitudinal central axis 112 as captive portion 116.First set 117 of first structures 120 a and second set 119 of secondstructures 120 b do not overlap along longitudinal central axis 112.Second set 119 of second structures 120 b is closer to captive end 118than first set 117 of first structures 120 a. First set 117 of firststructures 120 a has a first axial compliance coefficient alonglongitudinal central axis 112. Second set 119 of second structures 120 bhas a second axial compliance coefficient along longitudinal centralaxis 112. The first axial compliance coefficient of first set 117 offirst structures 120 a is greater than the second axial compliancecoefficient of second set 119 of second structures 120 b. The precedingsubject matter of this paragraph characterizes example 1 of the presentdisclosure.

The first axial compliance coefficient being greater than the secondaxial compliance coefficient allows first structures 120 a to bend morethan second structures 120 b when the same axial force (i.e., the forcealong longitudinal central axis 112) is applied to each of first set 117of first structures 120 a and second set 119 of second structures 120 b.More specifically, when the same axial force is applied to the ends offirst structures 120 a and to the ends of second structures 120 b, firststructures 120 a will bend more along longitudinal central axis 112 thanof second structures 120 b. This bending difference is relied on toavoid exceeding static friction between the ends of first structures 120a and to the ends of second structures 120 b and a structure which theseends engage. For example, shank 110 may be retained in the receiver. Ifstatic friction is not lost, shank 110 will not walk out of receiver.Without being restricted to any particular theory, it is believed thatduring operation of shank 110, shank 110 experiences less angulardeformation closer to captive end 118 than further away from captive end118 such as the opposite end of captive portion 116. This difference inangular deformations results is further described below with referencesto FIGS. 2A-2C, 3A-3H, 4A-4C, 5A-5B, and 6A-6B.

As used herein, a longitudinal central axis is a line (which may or maynot be straight) passing through the centroid of each cross-section ofan object, where the centroid (geometric center) of a two-dimensionalregion is the arithmetic-mean or “average” position of all the points inthe two-dimensional region.

FIG. 2A is a schematic sectional view of receiver 30 supporting shank10, which is subjected to a lateral force while being rotated. Thelateral force may be a result of moving shank 10, which may be an endmill, for example, in a lateral direction and forcing shank 10 againstworkpiece 20. As a result of this lateral force, which may be defined asany force in a direction formal to longitudinal central axis 12, thecoupling between receiver 30 and shank 10 may be impacted. In thisexample, compression in area 1 may be greater than compression in area3, while compression in area 2 may less than compression in area 2.These compressions are defined as a force with which receiver 30compresses on shank 10 and vice versa. This difference in compressionmay result in slip conditions in areas 2 and 3 due to the loss in staticfriction and various axial forces in the identified area. When the slipoccurs, a portion of shank 10 extends from receiver in area 3 as shownin FIG. 2A. As receiver 30 rotates around its longitudinal central axis12 the locations of area 1 and area 3 interchange with additionalportions of shank 10 slipping out of receiver 30 at every turn. Thisphenomenon may be referred to as “walk out”. A similar phenomenon occursfor when receiver 30 and longitudinal central axis 12 vibrate withrespect to each other in a direction along the lateral force, which maybe perpendicular to longitudinal central axis 12. This example isillustrated in FIGS. 2B and 2C.

FIGS. 3A-3D and, separately, FIGS. 3E-3H illustrate that addingstructures to a shank increases the axial compliance of the shank alongits longitudinal central axis and helps to reduce or completely mitigatethe “walk out” phenomenon described above. Specifically, FIGS. 3A-3Dillustrate receiver 30 engaging shank 10 without any structures eitheron receiver 30 or shank 10. While receiver 30 and shank 10 have someaxial compliance due to the elastic deformation of receiver 30 and shank10, this compliance has proved to be insufficient to prevent the “walkout” phenomenon for many applications and operating conditions.

FIG. 3A illustrates a state before applying any lateral forces. In thisstate, first receiver reference point 31 a is aligned with first shankreference point 11 a. Separately, second receiver reference point 31 bis aligned with second shank reference point 11 b.

FIG. 3B illustrates a state when a lateral force is first applied in thedirection from first shank reference point 11 a to second shankreference point 11 b. As described above with reference to FIG. 1A, thisforce may cause a slip of shank 10 with respect to receiver 30 such thatfirst shank reference point 11 a may move to the left from firstreceiver reference point 31 a and become misaligned as shown in FIG. 3B.This slip may result in first shank reference point 11 a being forcedaway from first receiver reference point 31 a and loss of staticfriction between first shank reference point 11 a and first receiverreference point 31 a. The elastic deformation of shank 10 and receiver30 may be another contributing factor. Second receiver reference point31 b may remain aligned with second shank reference point 11 b or atleast may slip less than first shank reference point 11 a relative tofirst receiver reference point 31 a.

FIG. 3C illustrates a state in which shank 10 and receiver 30 experiencea force in an opposite direction relative to the state shown in FIG. 3B.This change in the force orientation may be due to the vibration ofshank 10 and receiver 30 or due to the rotation of shank 10 and receiver30. As shown in FIG. 3C, the force is now directed from second shankreference point 11 b to first shank reference point 11 a. This force maycause a slip of shank 10 with respect to receiver 30 such that secondshank reference point 11 b now may move to the left from second receiverreference point 31 b and become misaligned. This slip may result insecond shank reference point 11 b being forced away from second receiverreference point 31 b and loss of static friction between second shankreference point 11 b and second receiver reference point 31 b. Theelastic deformation of shank 10 and receiver 30 may be anothercontributing factor. The relative position of first receiver referencepoint 131 a to first shank reference point 11 a may remain or at leastmay change less than the relative position of second shank referencepoint 11 b and second receiver reference point 31 b. It should be notedthat in this state first shank reference point 11 a may not move backinto its original position relative to first receiver reference point 31a shown in FIG. 3A. As such, on average, shank 10 extends further out ofreceiver 30 as this assembly moves from the state shown in FIG. 3A tothe state shown in FIG. 3B and then to the state shown in FIG. 3C, andso on.

FIG. 3D illustrates a state in which shank 10 and receiver 30 experiencea force in an opposite direction relative to the state shown in FIG. 3C.This direction is the same as shown in FIG. 3B. This force may cause afurther slip of shank 10 with respect to receiver 30 such that firstshank reference point 11 a may move further to the left from firstreceiver reference point 31 a in comparison to the orientations of firstshank reference point 11 a and first receiver reference point 31 a shownin FIGS. 3B and 3C.

FIGS. 3E-3H illustrate shank 110 having structures that are engaged byreceiver 130. These structures have an axial compliance coefficient,which may be much greater that the axial compliance coefficient asimilar shank without such structures. With this high axial compliancecoefficient, the structures can bend and help to prevent the loss ofstatic friction.

FIG. 3E illustrates a state before applying any lateral forces. In thisstate, first receiver reference point 131 a is aligned with first shankreference point 111 a. Separately, second receiver reference point 131 bis aligned with second shank reference point 111 b. The structures mayextend in a direction substantially normal to longitudinal central axis112.

FIG. 3F illustrates a state when a lateral force is first applied in thedirection from first shank reference point 111 a to second shankreference point 111 b. This force may cause first shank reference point111 a to move to the left from its original position shown in FIG. 3E.However, the structures of shank 110 will bend and move in the samedirection and by the same amount. As such, first shank reference point111 a remains aligned with respect to first receiver reference point 131a. Second receiver reference point 131 b also remains aligned withsecond shank reference point 111 b.

FIG. 3G illustrates a state in which shank 110 and receiver 130experience a force in an opposite direction relative to the state shownin FIG. 3F. This change in the force orientation may be due to thevibration of shank 110 and receiver 130 or due to the rotation of shank110 and receiver 130. As shown in FIG. 3G, the force is now directedfrom second shank reference point 111 b to first shank reference point111 a. This force may cause second shank reference point 111 b to moveto the left from its original position shown in FIG. 3E and from theposition shown in FIG. 3F. However, the structures of shank 110 willbend and move in the same direction and by the same amount. As such,second shank reference point 111 b remains aligned with respect tosecond receiver reference point 131 b. First receiver reference point131 a also remains aligned with first shank reference point 111 c. Assuch, while on average, shank 110 extends further out of receiver 130 asin the state shown in FIGS. 3F and 3G in comparison to FIG. 3E, theextension processes effectively stops once the force is initiallyapplied. In other words, moving from the state shown in FIG. 3F to thestate shown in FIG. 3G, does not further extend shank 110 out ofreceiver 130, at least on average.

FIG. 3H illustrates a state in which shank 110 and receiver 130experience a force in an opposite direction relative to the state shownin FIG. 3G. This direction is the same as shown in FIG. 3F. This forcemay cause first shank reference point 111 a to move to the left from itsoriginal position shown in FIGS. 3E and 3G. However, the structures ofshank 110 will bend and move in the same direction and by the sameamount. As such, first shank reference point 111 a remains aligned withrespect to first receiver reference point 131 a. Second receiverreference point 131 b also remains aligned with second shank referencepoint 111 b. The state shown in FIG. 3H is effectively the same as thestate shown in FIG. 3F.

Various bending examples of shank 110 and receiver 130 will now bedescribed with reference to FIGS. 4A-4C. FIG. 4A is a schematic sectionview of shank 110 and receiver 130 that is not bend (e.g., not subjectedto any lateral force). FIG. 4B is a schematic section view of shank 110and receiver 130 subjected exhibiting a constant bend angle (identifiedas α) along longitudinal central axis 112. This example may correspondto bending of shank 110 and receiver 130 at a single point alonglongitudinal central axis 112 and presented as a reference only. Withoutbeing restricted to any particular theory, it is believed that thisexample may not represent the actual bending condition when a lateralforce is applied to shank 110.

FIG. 4C is a schematic section view of shank 110 and receiver 130subjected exhibiting a variable angle deformation. This example maycorrespond to bending of shank 110 and receiver 130 over multiple pointsalong longitudinal central axis 112 or even over the entire length ofshank 110 and receiver 130 along longitudinal central axis 112.Specifically, the bend angle (identified as (β2) is greater in area 402near receiving end 138 than the bend angle (identified as (β1) in area401 farther away from receiving end 138 than area 402. It should benoted that receiving end 138 of receiver 130 is aligned with the end ofcaptive portion 116 of shank 110 opposite of captive end 118. It shouldbe also noted that bending of shank 110 and receiver 130 alonglongitudinal central axis 112 may be uniform (e.g., a constant increaseover a different length along longitudinal central axis 112) ornon-uniform (e.g., a variable increase over a different length alonglongitudinal central axis 112). Both uniform and non-uniform bending mayproduce different bend angles as these angles identified in FIG. 4C.Effects of bend angles β1 and β2 being different in areas 401 and 402will now be described with reference to FIGS. 5A-5B and 6A-6B. Forclarity, the structures enhancing the axial compliance of shank 110 arenot shown in FIGS. 5A-5B and 6A-6B.

FIG. 5A is a schematic section view of area 401 having bend angle β1.Various points have been identified in this view for illustration, suchas point A (element 420), point B (element 422), point C (element 424),point D (element 426), point E (element 428), and point F (element 430).Some of this points are also shown in FIG. 5B, which is expanded view ofa portion of area 401. The same points are also shown in FIGS. 6A and6B. As shank 110 and receiver 130 deforms by bend angle β1, a cornerinitially corresponding to point D moves to the position correspondingto point B. Bend angle β1 may be also presented as angle DAB. In thisexample, line BC extends perpendicular to line AC (or line AD). As such,angle CBD is equal to bend angle β1 based on equivalence of trianglesCAD and CBD. The extension distance in this example is shown as EF,which depends on angle CBD and, as a result, on bend angle β1. When thebend angle increases, e.g., moving from bend angle β1 shown in FIGS.5A-5B to bend angle β2 shown in FIGS. 6A-6B, the extension distance alsoincreases. As such, the extension distance varies along longitudinalcentral axis 112 of interior space 136. If slip is allowed, as inconventional assemblies, slip distances will be also different alonglongitudinal central axis 112 and may generally correspond to theextension distances shown in FIGS. 4, 5A-5B, and 6A-6B.

In order to accommodate different extension distances along longitudinalcentral axis 112 without causing the slip (e.g., exceeding staticfriction), structures of shank 110 may have different axial compliancecoefficients along longitudinal central axis 112. For purposes of thisdisclosure, an axial compliance coefficient is defined as structure'sability to bend when an axial force is applied to the end of thisstructure. During operation of shank 110, this end of the structure maybe compressed against another surface, such as receiver 130, which mayapply the axial force to these ends. The axial force is applied alonglongitudinal central axis 112, which may be perpendicular to the lengthsof the structures (at least prior to bending the structures). It shouldbe noted that various other forced (in other directions) may act on thestructure at the same time.

A larger axial compliance coefficient allows the structure to bend morewithout losing static friction with a surface, against which thisstructure is pressed. For example, when two structures are pressedagainst a surface and the surface is slid in a direction substantiallynormal to the length of these structures, the structure with a smalleraxial compliance coefficient will slip (relative to the surface) beforethe structure with a larger axial compliance coefficient. Specifically,the force between the structure with a smaller axial compliancecoefficient and the surface will be greater than the force between thestructure with a larger axial compliance coefficient and the surface forthe same degree of bend. As such, the force between the structure with asmaller axial compliance coefficient and the surface will exceed staticfriction earlier than the structure with a larger axial compliancecoefficient. As such, one or more structures with a larger axialcompliance coefficient may be positioned in areas where the relativemotion between two components (e.g., a receiver and shank) in the axialdirection is larger.

First structures 120 a extend away from longitudinal central axis 112 ina direction normal to longitudinal central axis 112. In some examples,all first structures 120 a extend in this direction. Alternatively, oneor more of first structures 120 a may extend in a different direction,which is not normal to longitudinal central axis 112. Furthermore,second structures 120 b extend away from longitudinal central axis 112in a direction normal to longitudinal central axis 112. In someexamples, all second structures 120 b extend in this direction.Alternatively, one or more of second structures 120 b may extend in adifferent direction, which is not normal to longitudinal central axis112. Those skilled in the art would understand that directions alongwhich first structures 120 a and second structures 120 b extendinitially (e.g., prior to applying the lateral force) may change duringoperation of shank 110 (e.g., when the lateral force is applied).

First set 117 of first structures 120 a and second set 119 of secondstructures 120 b are each half as long along longitudinal central axis112 as captive portion 116. First set 117 of first structures 120 a andsecond set 119 of second structures 120 b do not overlap alonglongitudinal central axis 112. In other words, first structures 120 aand second structures 120 b may be the only such structures of shank110. Captive portion 116 may be the only portion of shank 110 used toengage another components, such as a receiver. Even though first set 117of first structures 120 a and second set 119 of second structures 120 bhave the same length along longitudinal central axis 112, thecharacteristics (at least the axial compliance coefficients) of thesesets are different.

Second set 119 of second structures 120 b is closer to captive end 118than first set 117 of first structures 120 a. Based on the bending modeldescribed above with reference to FIGS. 4C, 5A-5B, and 6A-6B, first set117 of first structures 120 a may experience greater axial deformationthat second set 119 of second structures 120 b due to their relativelocations. Because of that first set 117 of first structures 120 a has agreater axial compliance coefficient than second set 119 of secondstructures 120 b. More specifically, first set 117 of first structures120 a has a first axial compliance coefficient along longitudinalcentral axis 112 of interior space 136. Second set 119 of secondstructures 120 b has a second axial compliance coefficient alonglongitudinal central axis 112 of interior space 136. The first axialcompliance coefficient of first set 117 of first structures 120 a isgreater than the second axial compliance coefficient of second set 119of second structures 120 b. As such, first set 117 of first structures120 a may be easier to bend than second set 119 of second structures 120b. When the same force along longitudinal central axis 112 is applied toeach set of structures (i.e., to the ends of first structures 120 a and,separately, to the ends of second structures 120 b), first structures120 a will bend more than second structures 120 b on average. As such,for the same level of static friction, first structures 120 a can bendmore than second structures 120 b before slipping. This axial compliancecoefficient difference will help preventing slip conditions at the endof captive potion opposite of captive end 118 where the extensiondistance may be greater as described above with reference to FIGS. 4C,5A-5B, and 6A-6B.

Referring generally to FIGS. 1, 8A, 8B, 9A, and 9B, and particularly to,e.g., FIGS. 8B, 9A, and 9B, first set 117 of first structures 120 a andsecond set 119 of second structures 120 b are indirectly connectedtogether. The preceding subject matter of this paragraph characterizesexample 2 of the present disclosure, wherein example 2 includes thesubject matter of example 1, above.

Indirectly connecting of first set 117 of first structures 120 a andsecond set 119 of second structures 120 b supports these sets withrespect to each other, thereby maintaining mechanical and functionalintegrity of shank 110. Furthermore, this indirect connection allowstransferring loads (e.g., forces and torques) between first set 117 offirst structures 120 a and second set 119 of second structures 120 b.For example, second set 119 of second structures 120 b is closer tocaptive end 118 and may be indirectly connected to first set 117 offirst structures 120 a, which also connect second set 119 of secondstructures 120 b to other components of shank 110, such as cutting edge121.

Indirectly connecting first set 117 of first structures 120 a and secondset 119 of second structures 120 b may be a result of first set 117 offirst structures 120 a and second set 119 of second structures 120 bbeing monolithic. For example, all first structures 120 a and all secondstructures 120 b may be made from the same starting block of material.This type of shank 110 does not need a separate bonding operation duringits fabrication, may be stronger than shank 110 formed using variousbonding techniques, but may be more difficult to fabricate.Alternatively, one of first structures 120 a, which is immediatelyadjacent to second set 119 of second structures 120 b, may be monolithicwith one of second structures 120 b, which is immediately adjacent tofirst set 117 of first structures 120 a. For example, the end structureof first set 117 of first structures 120 a and the adjacent endstructure of second set 119 of second structures 120 b may be made ofthe same starting block of material. One or more other structures offirst set 117 of first structures 120 a and/or of second set 119 ofsecond structures 120 b may be indirectly bonded to this monolithiccenter portion using one or more bonding techniques. Furthermore, one offirst structures 120 a, which is immediately adjacent to second set 119of second structures 120 b, and one of second structures 120 b, which isimmediately adjacent to first set 117 of first structures 120 a, may beindirectly connected to each other using one or more bonding techniques.These structures may be supported by connectors, and these twoconnectors may be directly connected to each other. Some examples ofsuch bonding techniques include welding (using, e.g., a gas flame, anelectric arc, a laser, an electron beam, friction, and ultrasound),diffusion bonding, adhesive bonding, mechanical coupling, and the like.

FIGS. 9A and 9B schematically illustrates an example of indirectconnections of first set 117 of first structures 120 a and second set119 of second structures 120 b. One of first structures 120 a may be anend structure of first set 117 of first structures 120 a and may beadjacent to second set 119 of second structures 120 b. Each firststructure 120 a may be supported by one of first connectors 125 a, asshown in FIGS. 9A and 9B. First structure 120 a and first connector 125a may both have annular shapes. One of second structures 120 b may be anend structure of second set 119 of structure 120 b and may be adjacentto first set 117 of first structures 120 a. Each second structure 120 bmay be supported by one of second connectors 125 b. Second structure 120b and second connector 125 b may both have annular shapes.

One of first structures 120 a (an end structure of first set 117 offirst structures 120 a) may be indirectly connected to one of secondstructures 120 b (an end structure of second set 119 of secondstructures 120 b) via first connector 125 a and second connector 125 b.For example, first connector 125 a and second connector 125 b may bedirectly bonded to each other using one of suitable bonding techniques.First structure 120 a and first connector 125 a may be monolithic ordirectly bonded to each other. Second structure 120 b and secondconnector 125 b may be monolithic or directly bonded to each other. Insome examples, first connector 125 a may be monolithic with secondconnector 125 b, while first structure 120 a and second structure 120 bmay be directly bonded to first connector 125 a and second connector 125b, respectively, using one or more bonding techniques. It should benoted that while first connector 125 a and second connector 125 b maydirectly contact each other, first structure 120 a and second structure120 b are spaced apart from each other even though first structure 120 amay be indirectly connected to structure 120 b.

Referring generally to FIGS. 1, 8A, 8B, 9A, and 9B, and particularly to,e.g., FIG. 8B, first structures 120 a are indirectly connected togetherand second structures 120 b are indirectly connected together. Thepreceding subject matter of this paragraph characterizes example 3 ofthe present disclosure, wherein example 3 includes the subject matter ofexample 2, above.

Structures may be indirectly connected together within each set (e.g.,first structures 120 a are indirectly connected together via firstconnectors 125 a, and, similarly, second structures 120 b are indirectlyconnected together via second connectors 125 b) to ensure mechanical andfunctional integrity of that set of structures. Furthermore, thisindirect connection may allow transferring various loads between thestructures within the set (e.g., through their connectors that may bedirectly connected as, for example, described above with reference toFIGS. 9A and 9B). In some examples, the indirect connection between thestructures of the set may also impact the axial compliance coefficientof the structures. Without being restricted to any particular theory, itis believed that indirect connection of the structures within a set mayreduce the axial compliance coefficient of that set of structures incomparison to a similar set in which the structures are not connected toeach other.

Indirect connection among first structures 120 a and/or among secondstructures 120 b may be the result of the structures in one or both setsof structures being monolithic. In some examples, structures within oneset may be separate components that are indirectly bonded together(e.g., via their connectors) using one or more bonding techniques. Someexamples of such techniques include welding (using, e.g., a gas flame,an electric arc, a laser, an electron beam, friction, and ultrasound),diffusion bonding, adhesive bonding, mechanical coupling, and the like.Having separate structures that are later indirectly bonded into a setallows, in some examples, using structures with different materialcompositions, shapes, and/or other features that may be more difficultor impossible to achieve with monolithic sets of structures.

Referring generally to FIGS. 1, 8A, 8B, 9A, and 9B, and particularly to,e.g., FIG. 8B, first set 117 of first structures 120 a and second set119 of second structures 120 b are diffusion bonded together indirectly.The preceding subject matter of this paragraph characterizes example 4of the present disclosure, wherein example 4 includes the subject matterof any one of examples 1-3, above.

Diffusion bonding introduces minimal residual stress, plasticdeformation, and may be suitable for materials that cannot be bonded byother techniques (e.g., by liquid fusion). As such, diffusion bondingmay preserve the geometry and orientations of first structures 120 a infirst set 117 and second structures 120 b in second set 119 when firststructures 120 a in first set 117 and second structures 120 b in secondset 119 are diffusion bonded together indirectly. Furthermore, diffusionbonding allows using different materials for first structures 120 a infirst set 117 in comparison to materials of second structures 120 b insecond set 119 when, for example, first structures 120 a are monolithicwith their connectors and second structures 120 b are monolithic withtheir connectors.

Diffusion bonding is a solid-state welding technique capable of joiningsimilar and dissimilar metals based on solid-state diffusion. Diffusionbonding may involve compressing surfaces of two components at hightemperatures resulting in atoms of a first component to diffuse into thesecond component (e.g., driven by the concentration gradient) and atomsof the second component to diffuse into the first component.

When first set 117 of first structures 120 a and second set 119 ofsecond structures 120 b are diffusion bonded together indirectly,adjacent end structures of first set 117 of first structures 120 a andof second set 119 of second structures 120 b may be diffusion bondedtogether to each other indirectly. More specifically, these structuresmay be supported by connectors, and these two connectors may bediffusion bonded to each other directly.

FIGS. 9A and 9B schematically illustrates an example of indirectconnections of first set 117 of first structures 120 a and second set119 of second structures 120 b. One of first structures 120 a may be anend structure of first set 117 of first structures 120 a and may beadjacent to second set 119 of second structures 120 b. Each firststructure 120 a may be supported by one of first connectors 125 a andmay extend from first connector 125 a toward longitudinal central axis112, as shown in FIGS. 9A and 9B. First structure 120 a and firstconnector 125 a may both have annular shapes. One of second structures120 b may be an end structure of second set 119 of second structures 120b and may be adjacent to first set 117 of first structures 120 a. Eachsecond structure 120 b may be supported by one of second connectors 125b and may extend from second connector 125 b toward longitudinal centralaxis 112. Second structure 120 b and second connector 125 b may bothhave annular shapes.

One of first structures 120 a (an end structure of first set 117 offirst structures 120 a) may be indirectly connected to one of secondstructures 120 b (an end structure of second set 119 of secondstructures 120 b) via first connector 125 a and second connector 125 b.For example, first connector 125 a and second connector 125 b may bedirectly bonded to each other using one of suitable bonding techniques.First structure 120 a and first connector 125 a may be monolithic ordirectly bonded to each other. Second structure 120 b and secondconnector 125 b may be monolithic or directly bonded to each other. Insome examples, first connector 125 a may be monolithic with secondconnector 125 b, while first structure 120 a and second structure 120 bmay be directly bonded to first connector 125 a and second connector 125b, respectively, using one or more bonding techniques. It should benoted that while first connector 125 a and second connector 125 b maydirectly contact each other, first structure 120 a and second structure120 b are spaced apart from each other even though first structure 120 amay be indirectly connected to structure 120 b.

Referring generally to FIGS. 1, 8A, 8B, 9A, and 9B, and particularly to,e.g., FIG. 8B, first structures 120 a are diffusion bonded togetherindirectly and second structures 120 b are diffusion bonded togetherindirectly. The preceding subject matter of this paragraph characterizesexample 5 of the present disclosure, wherein example 5 includes thesubject matter of example 4, above.

Diffusion bonding introduces minimal residual stress, plasticdeformation, and may be suitable for materials that cannot be bonded byother techniques (e.g., liquid fusion). As such, diffusion bonding maypreserve the geometry and orientations of first structures 120 a infirst set 117 and second structures 120 b in second set 119 when firststructures 120 a are diffusion bonded together indirectly (e.g., throughsupported of first structures 120 a being diffusion bonded directly)and/or when second structures 120 b are diffusion bonded togetherindirectly (e.g., through supported of first structures 120 a beingdiffusion bonded directly). Furthermore, diffusion bonding allows usingdifferent materials for first structures 120 a in first set 117 incomparison to materials of second structures 120 b in second set 119when, for example, first structures 120 a are monolithic with theirconnectors and second structures 120 b are monolithic with theirconnectors.

Diffusion bonding is a solid-state welding technique capable of joiningsimilar and dissimilar metals based on solid-state diffusion. Diffusionbonding may involve compressing surfaces of two components at hightemperatures resulting in atoms of a first component to diffuse into thesecond component (e.g., driven by the concentration gradient) and atomsof the second component to diffuse into the first component.

When first structures 120 a are diffusion bonded together indirectly andsecond structures 120 b are diffusion bonded together indirectly,supports of first structures 120 a may be diffusion bonded togetherdirectly and/or supports of second structures 120 b may be diffusionbonded together directly. In some examples, first structures 120 a maybe diffusion bonded to their supports, which may be monolithic or bondedtogether using one or more bonding techniques, such as diffusionbonding. In some examples, second structures 120 b may be diffusionbonded to their supports, which may be monolithic or bonded togetherusing one or more bonding techniques, such as diffusion bonding. In someexamples, supports of first structures 120 a and supports of secondstructures 120 b are monolithic.

Referring generally to FIGS. 8A-8B and 9A-9B, and particularly to, e.g.,FIGS. 9A-9B, at least one of first structures 120 a is made of a firstmaterial. At least one of second structures 120 b is made of a secondmaterial. The first material is identical to the second material. Thepreceding subject matter of this paragraph characterizes example 6 ofthe present disclosure, wherein example 6 includes the subject matter ofany one of examples 1-5, above.

Materials of first structures 120 a and second structures 120 b effectmechanical properties of these structures and sets and, in particular,their axial compliance coefficients. For example, when all structures ofboth sets are made from the identical material, the difference in theaxial compliance coefficients between these two sets may be achieved bydifferent geometries of the structures or some other characteristics.Furthermore, when all structures of both sets are made from theidentical material, the entire shank 110 may be monolithic or may bebonded more easily than, for example, when materials of the two sets aredifferent. Alternatively, even though at one of first structures 120 ais made from the identical material as at least one of second structures120 b, other structures in these sets may be made from other materials,which may be used to tailor axial compliance coefficients of the setsand individual structures within the sets.

For purposes of these disclosure, the materials of different structuresare identical when material composition, morphology (e.g.,crystallinity), and other material characteristics of these structureare identical (or vary by less than 1%, for example). It should be notedthat the structures (made from the identical materials) may still havedifferent size, shape, and other geometric characteristics. In someexamples, all first structures 120 a are made of the first material.Furthermore, all second structures 120 b are made of the secondmaterial. In other words, all structures of shank 110 are made from theidentical material. Some examples of the first material and secondmaterial include titanium (e.g., for weight reduction, allowing forrapid changes in the rotational speed of the shank, preventingcorrosion, and/or using with high magnetic fields), beryllium-copperalloys (e.g., small structures, structures with micro-features),stainless steel (e.g., for weldability and/or corrosion resistance),tool steel (e.g., as a body material due to its high strength, hardness,and low cost), tungsten (e.g., for structures with a high compliancecoefficient or for body material to minimize bending). The selection ofthe materials may also ensure coupling (e.g., heat shrinking) betweenthe shank and, for example, receiver.

Referring generally to FIGS. 8A-8B and 9A-9B, and particularly to, e.g.,FIGS. 9A-9B, at least another one of first structures 120 a is made of athird material. At least another one of second structures 120 b is madeof a fourth material. The first material is different from the thirdmaterial. The second material is different from the fourth material. Thepreceding subject matter of this paragraph characterizes example 7 ofthe present disclosure, wherein example 7 includes the subject matter ofexample 6, above.

Different materials may be used for different first structures 120 a andfor different second structures 120 b to achieve the difference in theaxial compliance coefficients along longitudinal central axis 112 andspecific distribution of these axial compliance coefficients alonglongitudinal central axis 112. Furthermore, different materials may beused to achieve different static friction levels between structures andanother component engaging shank 110.

For purposes of these disclosure, the materials of different structuresare different when at least one of the material composition, morphology(e.g., crystallinity), or any other material characteristic of thesestructure differ (e.g., by at least 1%). For example, one structure in aset may receive a different heat treatment (e.g., annealing) or chemicaltreatment (e.g., coating with another material, carbonization, and thelike) than another structure in the same set. Alternatively, differentstructures of the same set may be formed from different materials, suchtool steel and tungsten, or titanium and beryllium-copper alloy, or toolsteel and stainless steel, and then indirectly bonded together to a set.In some examples, the third material may be the same as the fourthmaterial. Alternatively, the third material may different from thefourth material.

Referring generally to FIGS. 8A-8B and 9A-9B, and particularly to, e.g.,FIGS. 9A-9B, at least one of first structures 120 a is made of a firstmaterial. At least one of second structures 120 b is made of a secondmaterial. The first material is different from the second material. Thepreceding subject matter of this paragraph characterizes example 8 ofthe present disclosure, wherein example 8 includes the subject matter ofany one of examples 1-5, above.

Materials of first structures 120 a and second structures 120 b have aneffect on mechanical properties of these structures and sets and in,particular, on their axial compliance coefficients. For example, whenthe structures of two sets are made from different materials, thisdifference may be used to achieve different axial compliancecoefficients of these sets.

For example, the first material used for of first structures 120 a mayhave a lower elastic modulus than the second material used for of secondstructures 120 b. In some examples, the elastic modulus of the firstmaterial may be at least 5% less than that of the second material oreven at least 10% less. This difference in the elastic modulus mayresult in different axial compliance coefficients of the sets, i.e., thefirst axial compliance coefficient of first set 117 of first structures120 a being greater than the second axial compliance coefficient ofsecond set 119 of second structures 120 b. For example, the firstmaterial may be tool steel, while the second material may be tungsten.In another example, the first material may titanium, while the secondmaterial may be a beryllium-copper alloy. In yet another example, thefirst material may tool steel, while the second material may bestainless steel.

Referring generally to FIGS. 8A-8B and 9A-9B, and particularly to, e.g.,FIGS. 9A-9B, at least another one of first structures 120 a is made of athird material. At least another one of second structures 120 b is madeof a fourth material. The first material is identical to the thirdmaterial. The second material is identical to the fourth material. Thepreceding subject matter of this paragraph characterizes example 9 ofthe present disclosure, wherein example 9 includes the subject matter ofexample 8, above.

Forming multiple structure of the same set or even an entire set of thesame material may be more efficient from the shank fabricationstandpoint. Furthermore, the set may be monolithic. Yet, using differentmaterials for different sets may be help to achive different axialcompliance coefficients of different set. For example, the firstmaterial (and the third material) use for first structures 120 a mayhave a lower elastic modulus than the second material (and the fourthmaterial) used for second structures 120 b. For example, the firstmaterial may be tool steel, while the second material may be tungsten.In another example, the first material may titanium, while the secondmaterial may be a beryllium-copper alloy. In yet another example, thefirst material may tool steel, while the second material may bestainless steel. In some examples, all first structures 120 a is madefrom the same materials. Alternatively, at least one of first structures120 a is made from a material different from the first material (and thethird material). In some examples, all second structures 120 b is madefrom the same materials. Alternatively, at least one of secondstructures 120 b is made from a material different from the firstmaterial (and the third material).

Referring generally to FIGS. 7A, 8A-8B, and 9A-9B, and particularly to,e.g., FIG. 7A, first structures 120 a have a first combined averagewidth measured along longitudinal central axis 112 of shank 110. Secondstructures 120 b have a second combined average width measured alonglongitudinal central axis 112 of shank 110. The first combined averagewidth is identical to the second combined average width. The precedingsubject matter of this paragraph characterizes example 10 of the presentdisclosure, wherein example 10 includes the subject matter of any one ofexamples 1-9, above. A width of a structure is one of several factorsdetermining the axial compliance coefficient of this structure. With allother factors being the same, a wider structure may have a smaller axialcompliance coefficient than a similar but narrower structure. For a setincluding one or more structure, a combined average width of allstructures in the set may be used as one of many indicators of the axialcompliance coefficient of this set. However, this is not the onlyindicators. As such, even with first structures 120 a and secondstructures 120 b having the same combined average width, the first axialcompliance coefficient of first set 117 may be greater than the secondaxial compliance coefficient of second set 119 of second structures 120b.

For purposes of this disclosure, an individual average width of a singlestructure is defined as a ratio of the cross-sectional area (or half ofthe cross-sectional area for annular structures) to the length of thisstructure. The length is defined as its dimension in a directionperpendicular to longitudinal central axis 112. This definition accountsfor non-rectangular shapes of structures, such as structures havingtaper, shaped structure, and the like. Unless specifically, noted awidth of structure is referred to as an average width of this structure.The combined average width of a set is defined as a sum of individualaverage widths of all structures in this set. These individual averagewidths within the same set may all the same or different (e.g., increasefrom one end of the set to the other end).

When first structures 120 a and second structures 120 b have identicalcombined average widths, first structures 120 a and second structures120 b may have identical individual widths. Furthermore, identicalcombined average widths in two different sets may be achieved usingstructures having different individual widths. In one example, all firststructures 120 a may have identical individual widths. In the sameexample, all second structures 120 b may have identical individualwidths, which may be the same as the individual widths of firststructures 120 a. In this case, the number of first structures 120 a andsecond structures 120 b may be the same (in order for the combinedaverage widths to be the same for both sets). Furthermore, in this case,the difference between axial compliance coefficients of the two sets maybe attributed to different factors. Alternatively, all second structures120 b may have identical individual widths, but these individual widthsmay be different from individual widths of first structures 120 a. Inthis case, the number of first structures 120 a is different from thenumber of second structures 120 b (in order for the combined averagewidths to be the same for both sets). This difference in individualwidths and/or number of structures between first set 117 and second set119 may result in axial compliance coefficients of these two sets beingdifferent.

Furthermore, the individual widths of structures within each set maydiffer. For example, at least one of first structures 120 a may have adifferent individual width that at least another one of first structure120 a. In this example, all second structures 120 b may have identicalindividual widths. Alternatively, at least one of second structures 120b may have a different individual width that at least another one ofsecond structure 120 b. In another example, at least one of secondstructures 120 b may have a different individual width that at leastanother one of second structure 120 b. In this example, all firststructures 120 a may have the same individual width. Alternatively, atleast one of first structures 120 a may have a different individualwidth that at least another one of first structure 120 a.

Referring generally to FIGS. 7A, 8A-8B, and 9A-9B, and particularly to,e.g., FIG. 7A, first structures 120 a have a first combined averagewidth measured along longitudinal central axis 112 of shank 110. Secondstructures 120 b have a second combined average width measured alonglongitudinal central axis 112 of shank 110. The first combined averagewidth is different from the second combined average width. The precedingsubject matter of this paragraph characterizes example 11 of the presentdisclosure, wherein example 11 includes the subject matter of any one ofexamples 1-9, above. Different combined average widths of firststructures 120 a in first set 117 and second structures 120 b om secondset 119 may yield different axial compliance coefficients in these sets.FIG. 7A illustrates shank 110 that includes first structure 120 a andsecond structure 120 b. Individual width W₁ of first structure 120 a issmaller than individual width W₂ of second structure 120 b. As a result,first structure 120 a may have a larger axial compliance coefficientthan second structure 120 b. Scaling up this example to sets, the firstcombined average width of first structures 120 a is different from thesecond combined average width of second structures 120 b, resulting inthe first axial compliance coefficient of first set 117 of firststructures 120 a being different from the second axial compliancecoefficient of second set 119 of structures 120 b.

While the first combined average width is different from the secondcombined average width, individual widths of all structures in each setmay be the same or different. For example, the individual widths of allfirst structures 120 a may be the same. In this example, the individualwidths of all second structures 120 b may be the same but different fromthe individual widths of first structures 120 a. For example, theindividual widths of all second structures 120 b may greater than theindividual widths of first structures 120 a. Alternatively, theindividual widths of all second structures 120 b may be the same andalso the same as the individual widths of first structures 120 a.However, the number of first structures 120 a may be different from thenumber of second structures 120 b. For example, the number of secondstructures 120 b may greater than the number of first structures 120 a.In alternative examples, the individual widths of second structures 120b may different. Furthermore, the individual widths of all secondstructures 120 b may the same, but the individual widths of firststructures 120 a may different. For example, at least one of firststructures 120 a may have a different individual width that at leastanother one of first structure 120 a.

Referring generally to FIGS. 7A, 8A-8B, and 9A-9B, and particularly to,e.g., FIG. 7A, the first combined average width is less than the secondcombined average width. The preceding subject matter of this paragraphcharacterizes example 12 of the present disclosure, wherein example 12includes the subject matter of example 11, above. As noted above,different widths of the structures in first set 117 and second set 119may yield different axial compliance coefficients in these sets. Since agreater combined average width may result in a lower axial compliancecoefficient, the first combined average width may be less than thesecond combined average width in order for the first axial compliancecoefficient of first set 117 to be greater than the second axialcompliance coefficient of second set 119.

In some examples, the first combined average width is less than thesecond combined average width by at least about 5% or even at leastabout 50% or even 100%. The first combined average width may be lessthan the second combined average width due one or more factors, such asdifferent average individual widths of first structures 120 a and secondstructures 120 b, different number of first structures 120 a and secondstructures 120 b, or a combination of both. Furthermore, as describedabove, individual widths of all structures in each set may be the sameor different.

Referring generally to FIGS. 8A-8B, and 9A-9B, and particularly to,e.g., FIG. 7C, first structures 120 a have a first combined lengthmeasured perpendicular to longitudinal central axis 112 of shank 110.Second structures 120 b have a second combined length measuredperpendicular to longitudinal central axis 112 of shank 110. The firstcombined length is identical to the second combined length. Thepreceding subject matter of this paragraph characterizes example 13 ofthe present disclosure, wherein example 13 includes the subject matterof any one of examples 1-11, above.

A length of a structure is one of factors determining the axialcompliance coefficient of this structure. With all other factors beingthe same, a longer structure may have a larger axial compliancecoefficient than a similar, but shorter structure. For a set includingone or more structures, a combined length of all structures in the setis one of several factors affecting the axial compliance coefficient ofthe set. As noted above, the combined average width of the structures ineach set may be another factor affecting the axial compliancecoefficient. Accordingly, even with first structures 120 a and secondstructures 120 b having identical combined lengths, the first axialcompliance coefficient of first set 117 may be greater than the secondaxial compliance coefficient of second set 119 of second structures 120b. For example, first structures 120 a have a smaller combined averagewidth than second structures 120 b as, for example, shown in FIG. 7C.

For purposes of this disclosure, an individual length of a structure isdefined as its dimension in a direction perpendicular to longitudinalcentral axis 112 measured from the base of the structure to the tip thestructure. FIG. 7A identifies length (L) of one structure. The base ofthe structure may be its connector. The tip of the structure may be apart of the surface engaging another component, e.g., a shank, duringoperation of shank 110. The combined length of a set is defined as a sumof individual lengths of all structures in this set. All structureswithin the same set have identical individual lengths. Furthermore,first structures 120 a and second structures 120 b have identicalindividual lengths. In other words, all structures of shank 110 haveidentical individual lengths. When the number of first structures 120 ais identical to the number of second structures 120 b, the firstcombined length is identical to the second combined length. In thiscase, the difference between axial compliance coefficients of the twosets may be attributed to other factors (e.g., different combinedaverage widths of first set 117 and second set 119).

Referring generally to FIGS. 8A-8B, and 9A-9B, and particularly to,e.g., FIG. 7D and 7E, first structures 120 a have a first combinedlength measured perpendicular to longitudinal central axis 112 of shank110. Second structures 120 b have a second combined length measuredperpendicular to longitudinal central axis 112 of shank 110. The firstcombined length is different from the second combined length. Thepreceding subject matter of this paragraph characterizes example 14 ofthe present disclosure, wherein example 14 includes the subject matterof any one of examples 1-11, above. Different combined lengths of firststructures 120 a in first set 117 and of second structures 120 b insecond set 119 may yield different axial compliance coefficients forthese sets of structures.

While the first combined length of first structures 120 a may bedifferent from the second combined length of second structures 120 b,individual lengths of all structures in both sets are identical.Accordingly, the number of first structures 120 a may be different fromthe number of second structures 120 b. For example, the number of secondstructures 120 b may be fewer than the number of first structures 120 a,as illustrated in FIG. 7E. In this example, individual widths of secondstructures 120 b are greater than individual widths of first structures120 a. It should be noted that in this example the first combinedaverage width may be the same as the second combined average width. Forexample, individual widths of second structures 120 b may be twicegreater than individual widths of first structures 120 a while there maybe twice fewer second structures 120 b than first structures 120 a.Alternatively, the number of second structures 120 b may be greater thanthe number of first structures 120 a, as illustrated in FIG. 7D.Individual widths of second structures 120 b may be the same asindividual widths of first structures 120 a as shown in FIG. 7D ordifferent. It should be noted that in both examples shown in FIGS. 7Dand 7E, the first axial compliance coefficient of first set 117 of firststructures 120 a is greater than the second axial compliance coefficientof second set 119 of the second structures 120 b.

Referring generally to FIGS. 8A-8B, and 9A-9B, and particularly to,e.g., FIG. 7E, the first combined length is greater than the secondcombined length. The preceding subject matter of this paragraphcharacterizes example 15 of the present disclosure, wherein example 15includes the subject matter of example 14, above.

As noted above, different combined lengths of first structures 120 a andsecond structures 120 b may yield different axial compliancecoefficients for their corresponding sets. Specifically, if the firstcombined length of first structures 120 a is greater than the secondcombined length of second structures 120 b, the first axial compliancecoefficient of first set 117 may be greater than the second axialcompliance coefficient of second set 119 as, for example, shown in FIG.7E.

In some examples, the first combined length is greater than the secondcombined length by at least about 5%. In other examples, the firstcombined length is greater than the second combined length by at leastabout 50%. In still other examples, the first combined length is greaterthan the second combined length by at least about 100%. When the firstcombined length is greater than the second combined length, this is dueto a larger number of first structures 120 a than of second structures120 b.

Referring generally to FIGS. 7B, 8A-8B, and 9A-9B, and particularly to,e.g., FIG. 7B, first structures 120 a have a first combined camberangle. Second structures 120 b have a second combined camber angle. Thefirst combined camber angle is identical to the second combined camberangle. The preceding subject matter of this paragraph characterizesexample 16 of the present disclosure, wherein example 16 includes thesubject matter of any one of examples 1-11, 13, or 14, above.

A camber angle of a structure is one of factors determining the axialcompliance coefficient of this structure. With all other factors beingthe same, a structure with a smaller camber angle may have a largeraxial compliance coefficient than a similar structure with a largercamber angle. For a set including one or more structures, a combinedcamber angle of all structures in the set may be used as one of manyindicators of the axial compliance coefficient of that set. As notedabove, the widths and lengths of structures in each set may otherindicators of the axial compliance coefficient of that set. As such,even with first structures 120 a and second structures 120 b havingidentical combined camber angles, the first axial compliance coefficientof first set 117 may be greater than the second axial compliancecoefficient of second set 119 of second structures 120 b.

For purposes of this disclosure, an individual camber angle of astructure (one of first structures 120 a or second structures 120 b) isdefined as an angle between one side of a cross-section of thatstructure and an axis extending perpendicular to longitudinal centralaxis 112 in the plane of the cross-section. When both sides of thecross-section of the structure are symmetrical with respect to thataxis, either one of the sides may be used for determining the individualcamber angle of this structure. However, when the two sides are notsymmetrical, an average value of camber angles of both sides is used asan individual camber angle for the corresponding structure. Theindividual camber angle may be positive or negative, depending on theposition of the side relative to the axis extending perpendicular tolongitudinal central axis 112. Another way of determining whether theindividual camber angle is positive or negative is based on the anglebetween the side and longitudinal central axis 112. Specifically, if theside and longitudinal central axis 112 form an obtuse angle, then theindividual camber angle is positive. However, if the side andlongitudinal central axis 112 form an acute angle, then the individualcamber angle is negative. Finally, if the side and longitudinal centralaxis 112 are perpendicular, then the individual camber angle is zero. Acombined camber angle of a set is defined as a sum of all individualcamber angles for all structures in that set. FIG. 7B illustrates shank110 that has first structure 120 a and second structure 120 b. Camberangle α of first structure 120 a is positive and is greater than thecamber angle −α (which is a negative camber angle) of second structure120 b. Scaling up this example to sets, the first combined camber angleof first structures 120 a is different from the second combined camberangle of second structures 120 b resulting in the first axial compliancecoefficient of first set 117 being different from the second axialcompliance coefficient of second set 119.

When first structures 120 a and second structures 120 b have identicalcombined camber angles, first structures 120 a and second structures 120b may have identical individual camber angles. Furthermore, identicalcombined camber angles may be achieved in both sets with structureshaving different individual camber angles. In one example, all firststructures 120 a may have identical individual camber angles. In thesame example, all second structures 120 b may have identical individualcamber angles, which may be also identical to individual camber anglesof first structures 120 a. In this case, the number of first structures120 a and second structures 120 b may be identical. Furthermore, in thiscase, the difference between axial compliance coefficients of the twosets may be attributed to different factors (e.g., different combinedaverage widths of first set 117 and second set 119). Alternatively, allsecond structures 120 b may have identical individual camber angles, butthis camber angle may be different from the individual camber angle offirst structures 120 a (all first structures 120 a may have identicalindividual camber angles). In this case, the number of first structures120 a is different from the number of second structures 120 b. Thedifference in individual camber angles and numbers of the structures mayresult in different axial compliance coefficients of the two sets ofstructures.

Furthermore, individual camber angles of structures within each set maydiffer. For example, at least one of first structures 120 a may have adifferent individual camber angle that at least another one of firststructure 120 a. In this example, all second structures 120 b may haveidentical individual camber angles. Alternatively, at least one ofsecond structures 120 b may have a different individual camber anglethat at least another one of second structure 120 b. In another example,at least one of second structures 120 b may have a different individualcamber angle that at least another one of second structure 120 b. Inthis example, all first structures 120 a may have identical individualcamber angle. Alternatively, at least one of first structures 120 a mayhave a different individual camber angle that at least another one offirst structure 120 a.

Referring generally to FIGS. 8A-8B, and 9A-9B, and particularly to,e.g., FIG. 7B, first structures 120 a have a first combined camberangle. Second structures 120 b have a second combined camber angle. Thefirst combined camber angle is different from the second combined camberangle. The preceding subject matter of this paragraph characterizesexample 17 of the present disclosure, wherein example 17 includes thesubject matter of any one of examples 1-11, 13, or 14, above. Differentcombined camber angles of first set 117 and second set 119 may yielddifferent axial compliance coefficients in these sets.

While the first combined camber angle is different from the secondcombined camber angle, individual camber angles of all structures ineach set may be identical or different. For example, individual camberangles of all first structures 120 a may be identical. In this example,the individual camber angles of all second structures 120 b may beidentical to each other, but different from the individual camber anglesof first structures 120 a. For example, the individual camber angles ofall second structures 120 b may be less than the individual camberangles of first structures 120 a. Alternatively, the individual camberangles of all second structures 120 b may be identical to each other andalso identical to the individual camber angles of first structures 120a. However, the number of first structures 120 a may be different fromthe number of second structures 120 b. For example, the number of secondstructures 120 b may greater than the number of first structures 120 a.In alternative examples, the individual camber angles of secondstructures 120 b may different. Furthermore, the individual camberangles of all second structures 120 b may identical, but the individualcamber angles of first structures 120 a may different. For example, atleast one of first structures 120 a may have a different individualcamber angle that at least another one of first structure 120 a.

Referring generally to FIGS. 8A-8B, and 9A-9B, and particularly to,e.g., FIG. 7B, the first combined camber angle is less than the secondcombined camber angle. The preceding subject matter of this paragraphcharacterizes example 18 of the present disclosure, wherein example 18includes the subject matter of example 17, above. As noted above,different combined camber angles of first set 117 and second set 119 mayyield different axial compliance coefficients in these sets. Since agreater combined camber angle may result in a higher axial compliancecoefficient, the first combined camber angle may be greater than thesecond combined camber angle in order for the first axial compliancecoefficient of first set 117 to be greater than the second axialcompliance coefficient of second set 119.

In some examples, the first combined camber angle is greater than thesecond combined camber angle by at least about 5% or even at least about25% or even 50%. The first combined camber angle may be greater than thesecond combined camber angle due one or more factors, such as differentindividual camber angles of first structures 120 a and second structures120 b, different number of first structures 120 a and second structures120 b, or a combination of both. Furthermore, as described above, camberangles of all structures in each set may be the same or different.

Referring generally to FIGS. 8A-8B, shank 110 further comprising cuttingedge 121. First structures 120 a are closer to cutting edge 121 thansecond structures 120 b. The preceding subject matter of this paragraphcharacterizes example 19 of the present disclosure, wherein example 19includes the subject matter of any one of examples 1-18, above. Cuttingedge 121 may be a drill bit, a countersink, a counter-bore, a tap, adie, a milling cutter, a reamer, or a cold saw blade. Additionalexamples of cutting edge 121 include, but are not limited to a end mill,a roughing end mill, a ball nose cutter, a slab mill, a side-and-facecutter, a involute gear cutter, a hob, a thread mill, a face mill, a flycutter, a woodruff cutter, a hollow mill, a dovetail cutter, or a shellmill. When such examples of cutting edge 121 are used, an axial load maybe applied to the structures as described above.

Referring, e.g., to FIGS. 1, 8A, 8B, 9A, and 9B, shank 130 is disclosed.Shank 110 comprises captive portion 116 comprising a longitudinalcentral axis 112. Shank 110 also comprises captive end 118, first set117 of first structures 120 a, and second set 119 of second structures120 b. First structures 120 a extend away from longitudinal central axis112 in a direction normal to longitudinal central axis 112. Secondstructures 120 b extend away from longitudinal central axis 112 in adirection normal to longitudinal central axis 112. First set 117 offirst structures 120 a and second set 119 of second structures 120 b areindirectly connected together. The preceding subject matter of thisparagraph characterizes example 20 of the present disclosure.

Indirectly connecting first set 117 of first structures 120 a and secondset 119 of second structures 120 b supports these sets with respect toeach other, thereby maintaining mechanical and functional integrity ofshank 110. Furthermore, this indirect connection allows transferringloads (e.g., forces and torques) between first set 117 of firststructures 120 a and second set 119 of second structures 120 b.

Those skilled in the art will appreciate that first set 117 of firststructures 120 a and second set 119 of second structures 120 b will beconsidered indirectly connected together when first set 117 of firststructures 120 a and second set 119 of second structures 120 b are,e.g., monolithically formed of the same starting block of material, aslong as all individual structures are discrete, i.e., have the samelength. This type of shank 110 does not need a separate bondingoperation during its fabrication and may be stronger than shank 110formed using various bonding techniques. Alternatively, one of firststructures 120 a, which is immediately adjacent to second set 119 ofsecond structures 120 b, may be monolithic with one of second structures120 b, which is immediately adjacent to first set 117 of firststructures 120 a. For example, the end structure of first set 117 offirst structures 120 a and the adjacent end structure of second set 119of second structures 120 b may be made of the same starting block ofmaterial. One or more other structures of first set 117 of firststructures 120 a and/or of second set 119 of second structures 120 b maybe indirectly bonded to this monolithic center portion using one or morebonding techniques. Furthermore, one of first structures 120 a, which isimmediately adjacent to second set 119 of second structures 120 b, andone of second structures 120 b, which is immediately adjacent to firstset 117 of first structures 120 a, may be indirectly connected to eachother using one or more bonding techniques. These structures may besupported by connectors, monolithic with or bonded to their respectivestructures, and these connectors may be directly connected to eachother, e.g., through bonding or being monolithically formed, such thatthe structures are indirectly interconnected, meaning that all thestructures are discrete, i.e., have the same length. Some examples ofapplicable bonding techniques include welding (using, e.g., a gas flame,an electric arc, a laser, an electron beam, friction, and ultrasound),diffusion bonding, adhesive bonding, mechanical coupling, and the like.

Referring generally to FIGS. 1, 8A, 8B, 9A, and 9B, and particularly to,e.g., FIG. 8B, first structures 120 a are indirectly connected together.Second structures 120 b are indirectly connected together. The precedingsubject matter of this paragraph characterizes example 21 of the presentdisclosure, wherein example 21 includes the subject matter of example20, above.

Structures may be indirectly connected together within each set (e.g.,first structures 120 a are indirectly connected together via firstconnectors 125 a, and, similarly, second structures 120 b are indirectlyconnected together via second connectors 125 b) to ensure mechanical andfunctional integrity of each set of structures. As stated above, thoseskilled in the art will appreciate that structures are considered to beindirectly connected together if all of the structures are discrete,i.e., have the same length, once interconnected. Furthermore, thisindirect connection may allow transferring various loads between thestructures within the set (e.g., through their connectors that may bedirectly connected as, for example, described above with reference toFIGS. 9A and 9B).

Indirect connection among first structures 120 a and/or among secondstructures 120 b may be the result of the structures in one or both setsof structures being monolithic. In some examples, structures within oneset may be separate components that are indirectly bonded together(e.g., via their connectors) using one or more bonding techniques. Someexamples of such techniques include welding (using, e.g., a gas flame,an electric arc, a laser, an electron beam, friction, and ultrasound),diffusion bonding, adhesive bonding, mechanical coupling, and the like.Having separate structures that are later indirectly bonded into a setallows, in some examples, using structures with different materialcompositions, shapes, and/or other features that may be more difficultor impossible to achieve with monolithic sets of structures.

Referring generally to FIGS. 1, 8A, 8B, 9A, and 9B, and particularly to,e.g., FIG. 8B, first set 117 of first structures 120 a and second set119 of second structures 120 b are diffusion bonded together indirectly.The preceding subject matter of this paragraph characterizes example 22of the present disclosure, wherein example 22 includes the subjectmatter of any one of examples 20 or 21, above.

Diffusion bonding introduces minimal residual stress, plasticdeformation, and may be suitable for materials that cannot be bonded byother techniques (e.g., by liquid fusion). As such, diffusion bondingmay preserve the geometry and orientations of first structures 120 a infirst set 117 and second structures 120 b in second set 119 when firststructures 120 a in first set 117 and second structures 120 b in secondset 119 are diffusion bonded together indirectly. Furthermore, diffusionbonding allows using different materials for first structures 120 a infirst set 117 in comparison to materials of second structures 120 b insecond set 119 when, for example, first structures 120 a are monolithicwith their connectors and second structures 120 b are monolithic withtheir connectors.

Diffusion bonding is a solid-state welding technique capable of joiningsimilar and dissimilar metals based on solid-state diffusion. Diffusionbonding may involve compressing surfaces of two components at hightemperatures resulting in atoms of a first component to diffuse into thesecond component (e.g., driven by the concentration gradient) and atomsof the second component to diffuse into the first component.

When first set 117 of first structures 120 a and second set 119 ofsecond structures 120 b are diffusion bonded together indirectly,adjacent end structures of first set 117 of first structures 120 a andof second set 119 of second structures 120 b may be diffusion bondedtogether to each other indirectly. More specifically, these structuresmay be supported by connectors, and these two connectors may bediffusion bonded to each other directly.

FIGS. 9A and 9B schematically illustrates an example of indirectconnections of first set 117 of first structures 120 a and second set119 of second structures 120 b. One of first structures 120 a may be anend structure of first set 117 of first structures 120 a and may beadjacent to second set 119 of second structures 120 b. Each firststructure 120 a may be supported by one of first connectors 125 a andmay extend from first connector 125 a toward longitudinal central axis112, as shown in FIGS. 9A and 9B. First structure 120 a and firstconnector 125 a may both have annular shapes. One of second structures120 b may be an end structure of second set 119 of second structures 120b and may be adjacent to first set 117 of first structures 120 a. Eachsecond structure 120 b may be supported by one of second connectors 125b and may extend from second connector 125 b toward longitudinal centralaxis 112. Second structure 120 b and second connector 125 b may bothhave annular shapes.

One of first structures 120 a (an end structure of first set 117 offirst structures 120 a) may be indirectly connected to one of secondstructures 120 b (an end structure of second set 119 of secondstructures 120 b) via first connector 125 a and second connector 125 b.For example, first connector 125 a and second connector 125 b may bedirectly bonded to each other using one of suitable bonding techniques.First structure 120 a and first connector 125 a may be monolithic ordirectly bonded to each other. Second structure 120 b and secondconnector 125 b may be monolithic or directly bonded to each other. Insome examples, first connector 125 a may be monolithic with secondconnector 125 b, while first structure 120 a and second structure 120 bmay be directly bonded to first connector 125 a and second connector 125b, respectively, using one or more bonding techniques. It should benoted that while first connector 125 a and second connector 125 b maydirectly contact each other, first structure 120 a and second structure120 b are spaced apart from each other even though first structure 120 amay be indirectly connected to structure 120 b.

Referring generally to FIGS. 1, 8A, 8B, 9A, and 9B, and particularly to,e.g., FIG. 8B, first structures 120 a are diffusion bonded togetherindirectly and second structures 120 b are diffusion bonded togetherindirectly. The preceding subject matter of this paragraph characterizesexample 23 of the present disclosure, wherein example 23 includes thesubject matter of example 22, above.

Diffusion bonding introduces minimal residual stress, plasticdeformation, and may be suitable for materials that cannot be bonded byother techniques (e.g., liquid fusion). As such, diffusion bonding maypreserve the geometry and orientations of first structures 120 a infirst set 117 and second structures 120 b in second set 119 when firststructures 120 a are diffusion bonded together indirectly (e.g., throughsupported of first structures 120 a being diffusion bonded directly)and/or when second structures 120 b are diffusion bonded togetherindirectly (e.g., through supported of first structures 120 a beingdiffusion bonded directly). Furthermore, diffusion bonding allows usingdifferent materials for first structures 120 a in first set 117 incomparison to materials of second structures 120 b in second set 119when, for example, first structures 120 a are monolithic with theirconnectors and second structures 120 b are monolithic with theirconnectors.

Diffusion bonding is a solid-state welding technique capable of joiningsimilar and dissimilar metals based on solid-state diffusion. Diffusionbonding may involve compressing surfaces of two components at hightemperatures resulting in atoms of a first component to diffuse into thesecond component (e.g., driven by the concentration gradient) and atomsof the second component to diffuse into the first component.

When first structures 120 a are diffusion bonded together indirectly andsecond structures 120 b are diffusion bonded together indirectly,supports of first structures 120 a may be diffusion bonded togetherdirectly and/or supports of second structures 120 b may be diffusionbonded together directly. In some examples, first structures 120 a maybe diffusion bonded to their supports, which may be monolithic or bondedtogether using one or more bonding techniques, such as diffusionbonding. In some examples, second structures 120 b may be diffusionbonded to their supports, which may be monolithic or bonded togetherusing one or more bonding techniques, such as diffusion bonding. In someexamples, supports of first structures 120 a and supports of secondstructures 120 b are monolithic.

Referring generally to FIGS. 8A-8B and 9A-9B, and particularly to, e.g.,FIGS. 9A-9B, at least one of first structures 120 a is made of a firstmaterial. At least one of second structures 120 b is made of a secondmaterial. The first material is identical to the second material. Thepreceding subject matter of this paragraph characterizes example 24 ofthe present disclosure, wherein example 24 includes the subject matterof any one of examples 20-23, above.

Materials of first structures 120 a and second structures 120 b effectmechanical properties of these structures and sets and, in particular,their axial compliance coefficients. For example, when all structures ofboth sets are made from the identical material, the difference in theaxial compliance coefficients between these two sets may be achieved bydifferent geometries of the structures or some other characteristics.Furthermore, when all structures of both sets are made from theidentical material, the entire shank may be monolithic or may be bondedmore easily than, for example, when materials of the two sets aredifferent. Alternatively, even though at one of first structures 120 ais made from the identical material as at least one of second structures120 b, other structures in these sets may be made from other materials,which may be used to tailor axial compliance coefficients of the setsand individual structures within the sets.

For purposes of these disclosure, the materials of different structuresare identical when material composition, morphology (e.g.,crystallinity), and other material characteristics of these structureare identical (or vary by less than 1%, for example). It should be notedthat the structures (made from the identical materials) may still havedifferent size, shape, and other geometric characteristics. In someexamples, all first structures 120 a are made of the first material.Furthermore, all second structures 120 b are made of the secondmaterial. In other words, all structures of shank 110 are made from theidentical material. Some examples of the first material and secondmaterial include titanium (e.g., for weight reduction, allowing forrapid changes in the rotational speed of the shank, preventingcorrosion, and/or using with high magnetic fields), beryllium-copperalloys (e.g., small structures, structures with micro-features),stainless steel (e.g., for weldability and/or corrosion resistance),tool steel (e.g., as a body material due to its high strength, hardness,and low cost), tungsten (e.g., for structures with a high compliancecoefficient or for body material to minimize bending). The selection ofthe materials may also ensure coupling (e.g., heat shrinking) betweenthe shank and, for example, receiver.

Referring generally to FIGS. 8A-8B and 9A-9B, and particularly to, e.g.,FIGS. 9A-9B, at least another of first structures 120 a is made of athird material. At least another of second structures 120 b is made of afourth material. The first material is different from the thirdmaterial. The second material is different from the fourth material. Thepreceding subject matter of this paragraph characterizes example 25 ofthe present disclosure, wherein example 25 includes the subject matterof example 24, above.

Different materials may be used for different first structures 120 a andfor different second structures 120 b to achieve the difference in theaxial compliance coefficients along longitudinal central axis 112 andspecific distribution of these axial compliance coefficients alonglongitudinal central axis 112. Furthermore, different materials may beused to achieve different static friction levels between structures andanother component engaging shank 110.

For purposes of these disclosure, the materials of different structuresare different when at least one of the material composition, morphology(e.g., crystallinity), or any other material characteristic of thesestructure differ (e.g., by at least 1%). For example, one structure in aset may receive a different heat treatment (e.g., annealing) or chemicaltreatment (e.g., coating with another material, carbonization, and thelike) than another structure in the same set. Alternatively, differentstructures of the same set may be formed from different materials, suchtool steel and tungsten, or titanium and beryllium-copper alloy, or toolsteel and stainless steel, and then indirectly bonded together to a set.In some examples, the third material may be the same as the fourthmaterial. Alternatively, the third material may different from thefourth material.

Referring generally to FIGS. 8A-8B and 9A-9B, and particularly to, e.g.,FIGS. 9A-9B, at least one of first structures 120 a is made of a firstmaterial. At least one of second structures 120 b is made of a secondmaterial. The first material is different from the second material. Thepreceding subject matter of this paragraph characterizes example 26 ofthe present disclosure, wherein example 26 includes the subject matterof any one of examples 20-23, above.

Materials of first structures 120 a and second structures 120 b have aneffect on mechanical properties of these structures and sets and in,particular, on their axial compliance coefficients. For example, whenthe structures of two sets are made from different materials, thisdifference may be used to achieve different axial compliancecoefficients of these sets.

For example, the first material used for of first structures 120 a mayhave a lower elastic modulus than the second material used for of secondstructures 120 b. In some examples, the elastic modulus of the firstmaterial may be at least 5% less than that of the second material oreven at least 10% less. This difference in the elastic modulus mayresult in different axial compliance coefficients of the sets, i.e., thefirst axial compliance coefficient of first set 117 of first structures120 a being greater than the second axial compliance coefficient ofsecond set 119 of second structures 120 b. For example, the firstmaterial may be tool steel, while the second material may be tungsten.In another example, the first material may titanium, while the secondmaterial may be a beryllium-copper alloy. In yet another example, thefirst material may tool steel, while the second material may bestainless steel.

Referring generally to FIGS. 8A-8B and 9A-9B, and particularly to, e.g.,FIGS. 9A-9B, at least another of first structures 120 a is made of athird material. At least another of second structures 120 b is made of afourth material. The first material is identical to the third material.The second material is identical to the fourth material. The precedingsubject matter of this paragraph characterizes example 27 of the presentdisclosure, wherein example 27 includes the subject matter of example26, above.

Forming multiple structure of the same set or even an entire set of thesame material may be more efficient from the shank fabricationstandpoint. Furthermore, the set may be monolithic. Yet, using differentmaterials for different sets may be help to achive different axialcompliance coefficients of different set. For example, the firstmaterial (and the third material) use for first structures 120 a mayhave a lower elastic modulus than the second material (and the fourthmaterial) used for second structures 120 b. For example, the firstmaterial may be tool steel, while the second material may be tungsten.In another example, the first material may titanium, while the secondmaterial may be a beryllium-copper alloy. In yet another example, thefirst material may tool steel, while the second material may bestainless steel. In some examples, all first structures 120 a is madefrom the same materials. Alternatively, at least one of first structures120 a is made from a material different from the first material (and thethird material). In some examples, all second structures 120 b is madefrom the same materials. Alternatively, at least one of secondstructures 120 b is made from a material different from the firstmaterial (and the third material).

Referring generally to FIGS. 7A, 8A-8B, and 9A-9B, and particularly to,e.g., FIG. 7A, first structures 120 a have a first combined averagewidth measured along longitudinal central axis 112 of shank 110. Secondstructures 120 b have a second combined average width measured alonglongitudinal central axis 112 of shank 110. The first combined averagewidth is identical to the second combined average width. The precedingsubject matter of this paragraph characterizes example 28 of the presentdisclosure, wherein example 28 includes the subject matter of any one ofexamples 20-27, above.

A width of a structure is one of several factors determining the axialcompliance coefficient of this structure. With all other factors beingthe same, a wider structure may have a smaller axial compliancecoefficient than a similar but narrower structure. For a set includingone or more structure, a combined average width of all structures in theset may be used as one of many indicators of the axial compliancecoefficient of this set. However, this is not the only indicators. Assuch, even with first structures 120 a and second structures 120 bhaving the same combined average width, the first axial compliancecoefficient of first set 117 may be greater than the second axialcompliance coefficient of second set 119 of second structures 120 b.

For purposes of this disclosure, an individual average width of a singlestructure is defined as a ratio of the cross-sectional area (or half ofthe cross-sectional area for annular structures) to the length of thisstructure. The length is defined as its dimension in a directionperpendicular to longitudinal central axis 112. This definition accountsfor non-rectangular shapes of structures, such as structures havingtaper, shaped structure, and the like. Unless specifically, noted awidth of structure is referred to as an average width of this structure.The combined average width of a set is defined as a sum of individualaverage widths of all structures in this set. These individual averagewidths within the same set may all the same or different (e.g., increasefrom one end of the set to the other end).

When first structures 120 a and second structures 120 b have identicalcombined average widths, first structures 120 a and second structures120 b may have identical individual widths. Furthermore, identicalcombined average widths in two different sets may be achieved usingstructures having different individual widths. In one example, all firststructures 120 a may have identical individual widths. In the sameexample, all second structures 120 b may have identical individualwidths, which may be the same as the individual widths of firststructures 120 a. In this case, the number of first structures 120 a andsecond structures 120 b may be the same (in order for the combinedaverage widths to be the same for both sets). Furthermore, in this case,the difference between axial compliance coefficients of the two sets maybe attributed to different factors. Alternatively, all second structures120 b may have identical individual widths, but these individual widthsmay be different from individual widths of first structures 120 a. Inthis case, the number of first structures 120 a is different from thenumber of second structures 120 b (in order for the combined averagewidths to be the same for both sets). This difference in individualwidths and/or number of structures between first set 117 and second set119 may result in axial compliance coefficients of these two sets beingdifferent.

Furthermore, the individual widths of structures within each set maydiffer. For example, at least one of first structures 120 a may have adifferent individual width that at least another one of first structure120 a. In this example, all second structures 120 b may have identicalindividual widths. Alternatively, at least one of second structures 120b may have a different individual width that at least another one ofsecond structure 120 b. In another example, at least one of secondstructures 120 b may have a different individual width that at leastanother one of second structure 120 b. In this example, all firststructures 120 a may have the same individual width. Alternatively, atleast one of first structures 120 a may have a different individualwidth that at least another one of first structure 120 a.

Referring generally to FIGS. 7A, 8A-8B, and 9A-9B, and particularly to,e.g., FIG. 7A, first structures 120 a have a first combined averagewidth measured along longitudinal central axis 112 of shank 110. Secondstructures 120 b have a second combined average width measured alonglongitudinal central axis 112 of shank 110. The first combined averagewidth is different from the second combined average width. The precedingsubject matter of this paragraph characterizes example 29 of the presentdisclosure, wherein example 29 includes the subject matter of any one ofexamples 20-27, above. Different combined average widths of firststructures 120 a in first set 117 and second structures 120 b om secondset 119 may yield different axial compliance coefficients in these sets.FIG. 7A illustrates shank 110 that has first structure 120 a and secondstructure 120 b. Individual width W₁ of first structure 120 a is smallerthan individual width W₂ of second structure 120 b. As a result, firststructure 120 a may have a larger axial compliance coefficient thansecond structure 120 b. Scaling up this example to sets, the firstcombined average width of first structures 120 a is different from thesecond combined average width of second structures 120 b resulting inthe first axial compliance coefficient of first set 117 being differentfrom the second axial compliance coefficient of second set 119.

While the first combined average width is different from the secondcombined average width, individual widths of all structures in each setmay be the same or different. For example, the individual widths of allfirst structures 120 a may be the same. In this example, the individualwidths of all second structures 120 b may be the same but different fromthe individual widths of first structures 120 a. For example, theindividual widths of all second structures 120 b may greater than theindividual widths of first structures 120 a. Alternatively, theindividual widths of all second structures 120 b may be the same andalso the same as the individual widths of first structures 120 a.However, the number of first structures 120 a may be different from thenumber of second structures 120 b. For example, the number of secondstructures 120 b may greater than the number of first structures 120 a.In alternative examples, the individual widths of second structures 120b may different. Furthermore, the individual widths of all secondstructures 120 b may the same, but the individual widths of firststructures 120 a may different. For example, at least one of firststructures 120 a may have a different individual width that at leastanother one of first structure 120 a.

Referring generally to FIGS. 7A, 8A-8B, and 9A-9B, and particularly to,e.g., FIG. 7A, the first combined average width is less than the secondcombined average width. The preceding subject matter of this paragraphcharacterizes example 30 of the present disclosure, wherein example 30includes the subject matter of example 29, above. As noted above,different widths of the structures in first set 117 and second set 119may yield different axial compliance coefficients in these sets. Since agreater combined average width may result in a lower axial compliancecoefficient, the first combined average width may be less than thesecond combined average width in order for the first axial compliancecoefficient of first set 117 to be greater than the second axialcompliance coefficient of second set 119.

In some examples, the first combined average width is less than thesecond combined average width by at least about 5% or even at leastabout 50% or even 100%. The first combined average width may be lessthan the second combined average width due one or more factors, such asdifferent average individual widths of first structures 120 a and secondstructures 120 b, different number of first structures 120 a and secondstructures 120 b, or a combination of both. Furthermore, as describedabove, individual widths of all structures in each set may be the sameor different.

Referring generally to FIGS. 8A-8B, and 9A-9B, and particularly to,e.g., FIG. 7C, first structures 120 a have a first combined lengthmeasured perpendicular to longitudinal central axis 112 of shank 110.Second structures 120 b have a second combined length measuredperpendicular to longitudinal central axis 112 of shank 110. The firstcombined length is identical to the second combined length. Thepreceding subject matter of this paragraph characterizes example 31 ofthe present disclosure, wherein example 31 includes the subject matterof any one of examples 20-29, above.

A length of a structure is one of factors determining the axialcompliance coefficient of this structure. With all other factors beingthe same, a longer structure may have a larger axial compliancecoefficient than a similar, but shorter structure. For a set includingone or more structures, a combined length of all structures in the setis one of several factors affecting the axial compliance coefficient ofthe set. As noted above, the combined average width of the structures ineach set may be another factor affecting the axial compliancecoefficient. Accordingly, even with first structures 120 a and secondstructures 120 b having identical combined lengths, the first axialcompliance coefficient of first set 117 may be greater than the secondaxial compliance coefficient of second set 119 of second structures 120b. For example, first structures 120 a have a smaller combined averagewidth than second structures 120 b as, for example, shown in FIG. 7C.

For purposes of this disclosure, an individual length of a structure isdefined as its dimension in a direction perpendicular to longitudinalcentral axis 112 measured from the base of the structure to the tip thestructure. FIG. 7A identifies length (L) of one structure. The base ofthe structure may be its connector. The tip of the structure may be apart of the surface engaging another component, e.g., a shank, duringoperation of shank 110. The combined length of a set is defined as a sumof individual lengths of all structures in this set. All structureswithin the same set have identical individual lengths. Furthermore,first structures 120 a and second structures 120 b have identicalindividual lengths. In other words, all structures of shank 110 haveidentical individual lengths. When the number of first structures 120 ais identical to the number of second structures 120 b, the firstcombined length is identical to the second combined length. In thiscase, the difference between axial compliance coefficients of the twosets may be attributed to other factors (e.g., different combinedaverage widths of first set 117 and second set 119).

Referring generally to FIGS. 8A-8B, and 9A-9B, and particularly to,e.g., FIG. 7D and 7E, first structures 120 a have a first combinedlength measured perpendicular to longitudinal central axis 112 of shank110. Second structures 120 b have a second combined length measuredperpendicular to longitudinal central axis 112 of shank 110. The firstcombined length is different from the second combined length. Thepreceding subject matter of this paragraph characterizes example 32 ofthe present disclosure, wherein example 32 includes the subject matterof any one of examples 20-29, above. Different combined lengths of firstset 117 and second set 119 may yield different axial compliancecoefficients in these sets.

While the first combined length of first structures 120 a may bedifferent from the second combined length of second structures 120 b,individual lengths of all structures in both sets are identical.Accordingly, the number of first structures 120 a may be different fromthe number of second structures 120 b. For example, the number of secondstructures 120 b may be fewer than the number of first structures 120 a,as illustrated in FIG. 7E. In this example, individual widths of secondstructures 120 b are greater than individual widths of first structures120 a. It should be noted that in this example the first combinedaverage width may be the same as the second combined average width. Forexample, individual widths of second structures 120 b may be twicegreater than individual widths of first structures 120 a while there maybe twice fewer second structures 120 b than first structures 120 a.Alternatively, the number of second structures 120 b may be greater thanthe number of first structures 120 a, as illustrated in FIG. 7D.Individual widths of second structures 120 b may be the same asindividual widths of first structures 120 a as shown in FIG. 7D ordifferent. It should be noted that in both examples shown in FIGS. 7Dand 7E, the first axial compliance coefficient of first set 117 of firststructures 120 a is greater than the second axial compliance coefficientof second set 119 of the second structures 120 b.

Referring generally to FIGS. 8A-8B, and 9A-9B, and particularly to,e.g., FIG. 7E, the first combined length is greater than the secondcombined length. The preceding subject matter of this paragraphcharacterizes example 33 of the present disclosure, wherein example 33includes the subject matter of example 32, above.

As noted above, different combined lengths of first structures 120 a andsecond structures 120 b may yield different axial compliancecoefficients for their corresponding sets. Specifically, if the firstcombined length of first structures 120 a is greater than the secondcombined length of second structures 120 b, the first axial compliancecoefficient of first set 117 may be greater than the second axialcompliance coefficient of second set 119 as, for example, shown in FIG.7E.

In some examples, the first combined length is greater than the secondcombined length by at least about 5%. In other examples, the firstcombined length is greater than the second combined length by at leastabout 50%. In still other examples, the first combined length is greaterthan the second combined length by at least about 100%. When the firstcombined length is greater than the second combined length, this is dueto a larger number of first structures 120 a than of second structures120 b.

Referring generally to FIGS. 8A-8B, and 9A-9B, and particularly to,e.g., FIG. 7B, first structures 120 a have a first combined camberangle. Second structures 120 b have a second combined camber angle. Thefirst combined camber angle is identical to the second combined camberangle. The preceding subject matter of this paragraph characterizesexample 34 of the present disclosure, wherein example 34 includes thesubject matter of any one of examples 20-29, 31, or 32, above.

A camber angle of a structure is one of factors determining the axialcompliance coefficient of this structure. With all other factors beingthe same, a structure with a smaller camber angle may have a largeraxial compliance coefficient than a similar structure with a largercamber angle. For a set including one or more structures, a combinedcamber angle of all structures in the set may be used as one of manyindicators of the axial compliance coefficient of that set. As notedabove, the widths and lengths of structures in each set may otherindicators of the axial compliance coefficient of that set. As such,even with first structures 120 a and second structures 120 b havingidentical combined camber angles, the first axial compliance coefficientof first set 117 may be greater than the second axial compliancecoefficient of second set 119 of second structures 120 b.

For purposes of this disclosure, an individual camber angle of astructure (one of first structures 120 a or second structures 120 b) isdefined as an angle between one side of a cross-section of thatstructure and an axis extending perpendicular to longitudinal centralaxis 112 in the plane of the cross-section. When both sides of thecross-section of the structure are symmetrical with respect to thataxis, either one of the sides may be used for determining the individualcamber angle of this structure. However, when the two sides are notsymmetrical, an average value of camber angles of both sides is used asan individual camber angle for the corresponding structure. Theindividual camber angle may be positive or negative, depending on theposition of the side relative to the axis extending perpendicular tolongitudinal central axis 112. Another way of determining whether theindividual camber angle is positive or negative is based on the anglebetween the side and longitudinal central axis 112. Specifically, if theside and longitudinal central axis 112 form an obtuse angle, then theindividual camber angle is positive. However, if the side andlongitudinal central axis 112 form an acute angle, then the individualcamber angle is negative. Finally, if the side and longitudinal centralaxis 112 are perpendicular, then the individual camber angle is zero. Acombined camber angle of a set is defined as a sum of all individualcamber angles for all structures in that set. FIG. 7B illustrates shank110 that has first structure 120 a and second structure 120 b. Camberangle α of first structure 120 a is positive and is greater than thecamber angle −α (which is a negative camber angle) of second structure120 b. Scaling up this example to sets, the first combined camber angleof first structures 120 a is different from the second combined camberangle of second structures 120 b resulting in the first axial compliancecoefficient of first set 117 being different from the second axialcompliance coefficient of second set 119.

When first structures 120 a and second structures 120 b have identicalcombined camber angles, first structures 120 a and second structures 120b may have identical individual camber angles. Furthermore, identicalcombined camber angles may be achieved in both sets with structureshaving different individual camber angles. In one example, all firststructures 120 a may have identical individual camber angles. In thesame example, all second structures 120 b may have identical individualcamber angles, which may be also identical to individual camber anglesof first structures 120 a. In this case, the number of first structures120 a and second structures 120 b may be identical. Furthermore, in thiscase, the difference between axial compliance coefficients of the twosets may be attributed to different factors (e.g., different combinedaverage widths of first set 117 and second set 119). Alternatively, allsecond structures 120 b may have identical individual camber angles, butthis camber angle may be different from the individual camber angle offirst structures 120 a (all first structures 120 a may have identicalindividual camber angles). In this case, the number of first structures120 a is different from the number of second structures 120 b. Thedifference in individual camber angles and numbers of the structures mayresult in different axial compliance coefficients of the two sets ofstructures.

Furthermore, individual camber angles of structures within each set maydiffer. For example, at least one of first structures 120 a may have adifferent individual camber angle that at least another one of firststructure 120 a. In this example, all second structures 120 b may haveidentical individual camber angles. Alternatively, at least one ofsecond structures 120 b may have a different individual camber anglethat at least another one of second structure 120 b. In another example,at least one of second structures 120 b may have a different individualcamber angle that at least another one of second structure 120 b. Inthis example, all first structures 120 a may have identical individualcamber angle. Alternatively, at least one of first structures 120 a mayhave a different individual camber angle that at least another one offirst structure 120 a.

Referring generally to FIGS. 8A-8B, and 9A-9B, and particularly to,e.g., FIG. 7B, first structures 120 a have a first combined camberangle. Second structures 120 b have a second combined camber angle. Thefirst combined camber angle is different from the second combined camberangle. The preceding subject matter of this paragraph characterizesexample 35 of the present disclosure, wherein example 35 includes thesubject matter of any one of examples 20-29, 31, or 32, above. Differentcombined camber angles of first set 117 and second set 119 may yielddifferent axial compliance coefficients in these sets.

While the first combined camber angle is different from the secondcombined camber angle, individual camber angles of all structures ineach set may be identical or different. For example, individual camberangles of all first structures 120 a may be identical. In this example,the individual camber angles of all second structures 120 b may beidentical to each other, but different from the individual camber anglesof first structures 120 a. For example, the individual camber angles ofall second structures 120 b may be less than the individual camberangles of first structures 120 a. Alternatively, the individual camberangles of all second structures 120 b may be identical to each other andalso identical to the individual camber angles of first structures 120a. However, the number of first structures 120 a may be different fromthe number of second structures 120 b. For example, the number of secondstructures 120 b may greater than the number of first structures 120 a.In alternative examples, the individual camber angles of secondstructures 120 b may different. Furthermore, the individual camberangles of all second structures 120 b may identical, but the individualcamber angles of first structures 120 a may different. For example, atleast one of first structures 120 a may have a different individualcamber angle that at least another one of first structure 120 a.

Referring generally to FIGS. 8A-8B, and 9A-9B, and particularly to,e.g., FIG. 7B, the first combined camber angle is less than the secondcombined camber angle. The preceding subject matter of this paragraphcharacterizes example 36 of the present disclosure, wherein example 36includes the subject matter of example 35 above. As noted above,different combined camber angles of first set 117 and second set 119 mayyield different axial compliance coefficients in these sets. Since agreater combined camber angle may result in a higher axial compliancecoefficient, the first combined camber angle may be greater than thesecond combined camber angle in order for the first axial compliancecoefficient of first set 117 to be greater than the second axialcompliance coefficient of second set 119.

In some examples, the first combined camber angle is greater than thesecond combined camber angle by at least about 5% or even at least about25% or even 50%. The first combined camber angle may be greater than thesecond combined camber angle due one or more factors, such as differentindividual camber angles of first structures 120 a and second structures120 b, different number of first structures 120 a and second structures120 b, or a combination of both. Furthermore, as described above, camberangles of all structures in each set may be the same or different.

Referring generally to FIGS. 8A-8B, shank 110 further comprising cuttingedge 121. First structures 120 a are closer to cutting edge 121 thansecond structures 120 b. The preceding subject matter of this paragraphcharacterizes example 37 of the present disclosure, wherein example 19includes the subject matter of any one of examples 20-36, above. Cuttingedge 121 may be a drill bit, a countersink, a counter-bore, a tap, adie, a milling cutter, a reamer, or a cold saw blade. Additionalexamples of cutting edge 121 include, but are not limited to an endmill, a roughing end mill, a ball nose cutter, a slab mill, aside-and-face cutter, a involute gear cutter, a hob, a thread mill, aface mill, a fly cutter, a woodruff cutter, a hollow mill, a dovetailcutter, or a shell mill. When such examples of cutting edge 121 areused, an axial load may be applied to the structures as described above.

Referring generally to FIGS. 1, 9A, and 9B, and particularly to, e.g.,FIG. 10 (blocks 1004 and 1008) method 1000 of forming shank 110 isprovided. Method 1000 comprises arranging first structures 120 a infirst set 117 and second structures 120 b in second set 119 such thatfirst structures 120 a and second structures 120 b extend away fromlongitudinal central axis 112 in a direction normal to longitudinalcentral axis 112. Method 1000 also comprises indirectly bonding firstset 117 of first structures 120 a to second set 119 of second structures120 b. The preceding subject matter of this paragraph characterizesexample 38 of the present disclosure.

Indirect bonding of the structures of first set 117 and second set 119may be performed after fabricating these structures (e.g.,individually), which allows using various materials, shapes, and otherfeatures for these structures. When first structures 120 a in first set117 and second structures 120 b in second set 119 are arranged, theengaging ends of these structures may be aligned such that these endsfollow a profile of an component that shank 110 is later engaged by. Insome examples, the profile may be a cylinder. The structures may bearranged using an alignment tool that has a similar profile. Forexample, the structures may be slid onto the alignment tool andindirectly bonded while being arranged on the tool, after which the toolmay be removed.

In some embodiments, prior to arrangement of first structures 120 a infirst set 117 and second structures 120 b in second set 119, firststructures 120 a may receive a different heat treatment (e.g.,annealing) or chemical treatment (e.g., coating with another material,carbonization, and the like) than second structures 120 b. In someembodiments, different heat and/or chemical treatment may be applied tostructures of the same set. Different treatments may be used to achievedifferent axial compliance coefficients between different structures.

Various bonding techniques may be used for indirectly bonding first set117 of first structures 120 a to second set 119 of second structures 120b. Some examples of such techniques include welding (using, e.g., a gasflame, an electric arc, a laser, an electron beam, friction, andultrasound), adhesive bonding, mechanical coupling, and the like. Aspecific example of diffusion bonding of the two sets is furtherdescribed below in more details. When the two sets are indirectly bondedtogether, each of these sets may be monolithic. Alternatively, at leastsome structure in one or both of these sets may be indirectly bonded toother structures of the same set. Furthermore, when the parts of the twosets, but not the entire two sets, are monolithic, these parts maypresent at the interface of the two sets and extend in both directionsfrom this interface along longitudinal central axis 112. Otherstructures of each set may be bonded to these parts.

In some embodiments, after indirectly bonding first set 117 of firststructures 120 a to second set 119 of second structures 120 b, first set117 of first structures 120 a and second set 119 of second structures120 b may be machined or grinded to ensure alignment of engagementsurfaces of first structures 120 a and second structures 120 b. Forexample, first structures 120 a and second structures 120 b may not besufficiently aligned after arranging first structures 120 a in first set117 and second structures 120 b in second set 119 and/or becomemisaligned while indirectly bonding first set 117 of first structures120 a to second set 119 of second structures 120 b. Machining and/orgrinding of at least the engagement surfaces ensures that these surfaceshave substantially the same level of engagement (e.g., compressionforce).

Referring generally to FIGS. 1, 9A, and 9B, and particularly to, e.g.,FIG. 10 (block 1012), method 1000 further comprises indirectly bondingfirst structures 120 a together and indirectly bonding second structures120 b of second set 119 together. The preceding subject matter of thisparagraph characterizes example 39 of the present disclosure, whereinexample 39 includes the subject matter of example 38 above.

Structures may be indirectly connected together within each set (e.g.,first structures 120 a are indirectly connected together via firstconnectors 125 a, and, similarly, second structures 120 b are indirectlyconnected together via second connectors 125 b) to ensure mechanical andfunctional integrity of that set of structures. Furthermore, thisindirect connection may allow transferring various loads between thestructures within the set (e.g., through their connectors that may bedirectly connected as, for example, described above with reference toFIGS. 9A and 9B). In some examples, the indirect connection between thestructures of the set may also impact the axial compliance coefficientof the structures. Without being restricted to any particular theory, itis believed that indirect connection of the structures within a set mayreduce the axial compliance coefficient of that set of structures incomparison to a similar set in which the structures are not connected toeach other. One example of a shank where the structures are notconnected to each other via connectors may include a housing insidewhich structures are captively retained.

Indirect connection among first structures 120 a and/or among secondstructures 120 b may be the result of the structures in one or both setsof structures being monolithic. In some examples, structures within oneset may be separate components that are indirectly bonded together(e.g., via their connectors) using one or more bonding techniques. Someexamples of such techniques include welding (using, e.g., a gas flame,an electric arc, a laser, an electron beam, friction, and ultrasound),diffusion bonding, adhesive bonding, mechanical coupling, and the like.Having separate structures that are later indirectly bonded into a setallows, in some examples, using structures with different materialcompositions, shapes, and/or other features that may be more difficultor impossible to achieve with monolithic sets of structures.

Referring generally to FIGS. 1, 9A, and 9B, and particularly to, e.g.,FIG. 10 (block 1012), indirectly bonding first structures 120 a togethercomprises indirectly diffusion bonding first structures 120 a together.Indirectly bonding second structures 120 b of second set 119 togethercomprises indirectly diffusion bonding second structures 120 b of secondset 119 together. The preceding subject matter of this paragraphcharacterizes example 40 of the present disclosure, wherein example 40includes the subject matter of example 39, above.

Diffusion bonding introduces minimal residual stress, plasticdeformation, and may be suitable for materials that cannot be bonded byother techniques (e.g., liquid fusion). As such, diffusion bonding maypreserve the geometry and orientations of first structures 120 a infirst set 117 and second structures 120 b in second set 119 when firststructures 120 a are diffusion bonded together indirectly (e.g., throughsupported of first structures 120 a being diffusion bonded directly)and/or when second structures 120 b are diffusion bonded togetherindirectly (e.g., through supported of first structures 120 a beingdiffusion bonded directly). Furthermore, diffusion bonding allows usingdifferent materials for first structures 120 a in first set 117 incomparison to materials of second structures 120 b in second set 119when, for example, first structures 120 a are monolithic with theirconnectors and second structures 120 b are monolithic with theirconnectors.

Diffusion bonding is a solid-state welding technique capable of joiningsimilar and dissimilar metals based on solid-state diffusion. Diffusionbonding may involve compressing surfaces of two components at hightemperatures resulting in atoms of a first component to diffuse into thesecond component (e.g., driven by the concentration gradient) and atomsof the second component to diffuse into the first component.

When first structures 120 a are diffusion bonded together indirectly andsecond structures 120 b are diffusion bonded together indirectly,supports of first structures 120 a may be diffusion bonded togetherdirectly and/or supports of second structures 120 b may be diffusionbonded together directly. In some examples, first structures 120 a maybe diffusion bonded to their supports, which may be monolithic or bondedtogether using one or more bonding techniques, such as diffusionbonding. In some examples, second structures 120 b may be diffusionbonded to their supports, which may be monolithic or bonded togetherusing one or more bonding techniques, such as diffusion bonding. In someexamples, supports of first structures 120 a and supports of secondstructures 120 b are monolithic.

Referring generally to FIGS. 1, 9A, and 9B, and particularly to, e.g.,FIG. 10 (block 1008), indirectly bonding first set 117 of firststructures 120 a to second set 119 of second structures 120 b comprisesindirectly diffusion bonding first set 117 of first structures 120 a tosecond set 119 of second structures 120 b. The preceding subject matterof this paragraph characterizes example 41 of the present disclosure,wherein example 41 includes the subject matter of any one of examples38-40, above.

Diffusion bonding introduces minimal residual stress, plasticdeformation, and may be suitable for materials that cannot be bonded byother techniques (e.g., by liquid fusion). As such, diffusion bondingmay preserve the geometry and orientations of first structures 120 a infirst set 117 and second structures 120 b in second set 119 when firststructures 120 a in first set 117 and second structures 120 b in secondset 119 are diffusion bonded together indirectly. Furthermore, diffusionbonding allows using different materials for first structures 120 a infirst set 117 in comparison to materials of second structures 120 b insecond set 119 when, for example, first structures 120 a are monolithicwith their connectors and second structures 120 b are monolithic withtheir connectors.

Diffusion bonding is a solid-state welding technique capable of joiningsimilar and dissimilar metals based on solid-state diffusion. Diffusionbonding may involve compressing surfaces of two components at hightemperatures resulting in atoms of a first component to diffuse into thesecond component (e.g., driven by the concentration gradient) and atomsof the second component to diffuse into the first component.

When first set 117 of first structures 120 a and second set 119 ofsecond structures 120 b are diffusion bonded together indirectly,adjacent end structures of first set 117 of first structures 120 a andof second set 119 of second structures 120 b may be diffusion bondedtogether to each other indirectly. More specifically, these structuresmay be supported by connectors, and these two connectors may bediffusion bonded to each other directly.

FIGS. 9A and 9B schematically illustrates an example of indirectconnections of first set 117 of first structures 120 a and second set119 of second structures 120 b. One of first structures 120 a may be anend structure of first set 117, which is adjacent to second set 119.First structure 120 a may be supported by one of first connectors 125 aand may extend from first connector 125 a toward longitudinal centralaxis 112 as shown in FIGS. 9A and 9B. First structure 120 a and firstconnector 125 a may both have annular shapes. One of second structures120 b may be an end structure of second set 119, which is adjacent tofirst set 117. Second structure 120 b may be supported by one of secondconnectors 125 b and may extend from second connector 125 b towardlongitudinal central axis 112. Second structure 120 b and secondconnector 125 b may both have annular shapes.

One of first structures 120 a (an end structure of first set 117 offirst structures 120 a) may be indirectly connected to one of secondstructures 120 b (an end structure of second set 119 of secondstructures 120 b) via first connector 125 a and second connector 125 b.For example, first connector 125 a and second connector 125 b may bedirectly bonded to each other using one of suitable bonding techniques.First structure 120 a and first connector 125 a may be monolithic ordirectly bonded to each other. Second structure 120 b and secondconnector 125 b may be monolithic or directly bonded to each other. Insome examples, first connector 125 a may be monolithic with secondconnector 125 b, while first structure 120 a and second structure 120 bmay be directly bonded to first connector 125 a and second connector 125b, respectively, using one or more bonding techniques. It should benoted that while first connector 125 a and second connector 125 b maydirectly contact each other, first structure 120 a and second structure120 b are spaced apart from each other even though first structure 120 amay be indirectly connected to structure 120 b.

Referring generally to FIGS. 8A-8B and 9A-9B, and particularly to, e.g.,FIGS. 9A-9B, at least one of first structures 120 a is made of a firstmaterial. At least one of second structures 120 b is made of a secondmaterial. The first material is identical to the second material. Thepreceding subject matter of this paragraph characterizes example 42 ofthe present disclosure, wherein example 42 includes the subject matterof any one of examples 38-41, above.

Materials of first structures 120 a and second structures 120 b effectmechanical properties of these structures and sets and, in particular,their axial compliance coefficients. For example, when all structures ofboth sets are made from the identical material, the difference in theaxial compliance coefficients between these two sets may be achieved bydifferent geometries of the structures or some other characteristics.Furthermore, when all structures of both sets are made from theidentical material, the entire shank may be monolithic or may be bondedmore easily than, for example, when materials of the two sets aredifferent. Alternatively, even though at one of first structures 120 ais made from the identical material as at least one of second structures120 b, other structures in these sets may be made from other materials,which may be used to tailor axial compliance coefficients of the setsand individual structures within the sets.

For purposes of these disclosure, the materials of different structuresare identical when material composition, morphology (e.g.,crystallinity), and other material characteristics of these structureare identical (or vary by less than 1%, for example). It should be notedthat the structures (made from the identical materials) may still havedifferent size, shape, and other geometric characteristics. In someexamples, all first structures 120 a are made of the first material.Furthermore, all second structures 120 b are made of the secondmaterial. In other words, all structures of shank 110 are made from theidentical material. Some examples of the first material and secondmaterial include titanium (e.g., for weight reduction, allowing forrapid changes in the rotational speed of the shank, preventingcorrosion, and/or using with high magnetic fields), beryllium-copperalloys (e.g., small structures, structures with micro-features),stainless steel (e.g., for weldability and/or corrosion resistance),tool steel (e.g., as a body material due to its high strength, hardness,and low cost), tungsten (e.g., for structures with a high compliancecoefficient or for body material to minimize bending). The selection ofthe materials may also ensure coupling (e.g., heat shrinking) betweenthe shank and, for example, receiver.

Referring generally to FIGS. 8A-8B and 9A-9B, and particularly to, e.g.,FIGS. 9A-9B, at least another of first structures 120 a is made of athird material. At least another of second structures 120 b is made of afourth material. The first material is different from the thirdmaterial. The second material is different from the fourth material. Thepreceding subject matter of this paragraph characterizes example 43 ofthe present disclosure, wherein example 43 includes the subject matterof example 42, above.

Different materials may be used for different first structures 120 a andfor different second structures 120 b to achieve the difference in theaxial compliance coefficients along longitudinal central axis 112 andspecific distribution of these axial compliance coefficients alonglongitudinal central axis 112. Furthermore, different materials may beused to achieve different static friction levels between structures andanother component, which may engage shank 110.

For purposes of these disclosure, the materials of different structuresare different when at least one of the material composition, morphology(e.g., crystallinity), or any other material characteristic of thesestructure differ (e.g., by at least 1%). For example, one structure in aset may receive a different heat treatment (e.g., annealing) or chemicaltreatment (e.g., coating with another material, carbonization, and thelike) than another structure in the same set. Alternatively, differentstructures of the same set may be formed from different materials, suchtool steel and tungsten, or titanium and beryllium-copper alloy, or toolsteel and stainless steel, and then indirectly bonded together to a set.In some examples, the third material may be the same as the fourthmaterial. Alternatively, the third material may different from thefourth material.

Referring generally to FIGS. 8A-8B and 9A-9B, and particularly to, e.g.,FIGS. 9A-9B, at least one of first structures 120 a is made of a firstmaterial. At least one of second structures 120 b is made of a secondmaterial. The first material is different from the second material. Thepreceding subject matter of this paragraph characterizes example 44 ofthe present disclosure, wherein example 44 includes the subject matterof any one of examples 38-37, above.

Materials of first structures 120 a and second structures 120 b have aneffect on mechanical properties of these structures and sets and in,particular, on their axial compliance coefficients. For example, whenthe structures of two sets are made from different materials, thisdifference may be used to achieve different axial compliancecoefficients of these sets.

For example, the first material used for of first structures 120 a mayhave a lower elastic modulus than the second material used for of secondstructures 120 b. In some examples, the elastic modulus of the firstmaterial may be at least 5% less than that of the second material oreven at least 10% less. This difference in the elastic modulus mayresult in different axial compliance coefficients of the sets, i.e., thefirst axial compliance coefficient of first set 117 of first structures120 a being greater than the second axial compliance coefficient ofsecond set 119 of second structures 120 b. For example, the firstmaterial may be tool steel, while the second material may be tungsten.In another example, the first material may titanium, while the secondmaterial may be a beryllium-copper alloy. In yet another example, thefirst material may tool steel, while the second material may bestainless steel.

Referring generally to FIGS. 8A-8B and 9A-9B, and particularly to, e.g.,FIGS. 9A-9B, at least another of first structures 120 a is made of athird material. At least another of second structures 120 b is made of afourth material. The first material is identical to the third material.The second material is identical to the fourth material. The precedingsubject matter of this paragraph characterizes example 45 of the presentdisclosure, wherein example 45 includes the subject matter of example44, above.

Forming multiple structure of the same set or even an entire set of thesame material may be more efficient from the shank fabricationstandpoint. Furthermore, the set may be monolithic. Yet, using differentmaterials for different sets may be help to achive different axialcompliance coefficients of different set. For example, the firstmaterial (and the third material) use for first structures 120 a mayhave a lower elastic modulus than the second material (and the fourthmaterial) used for second structures 120 b. For example, the firstmaterial may be tool steel, while the second material may be tungsten.In another example, the first material may titanium, while the secondmaterial may be a beryllium-copper alloy. In yet another example, thefirst material may tool steel, while the second material may bestainless steel. In some examples, all first structures 120 a is madefrom the same materials. Alternatively, at least one of first structures120 a is made from a material different from the first material (and thethird material). In some examples, all second structures 120 b is madefrom the same materials. Alternatively, at least one of secondstructures 120 b is made from a material different from the firstmaterial (and the third material).

Referring generally to FIGS. 7A, 8A-8B, and 9A-9B, and particularly to,e.g., FIG. 7A, first structures 120 a have a first combined averagewidth measured along longitudinal central axis 112 of shank 110. Secondstructures 120 b have a second combined average width measured alonglongitudinal central axis 112 of shank 110. The first combined averagewidth is identical to the second combined average width. The precedingsubject matter of this paragraph characterizes example 46 of the presentdisclosure, wherein example 46 includes the subject matter of any one ofexamples 38-45, above. A width of a structure is one of several factorsdetermining the axial compliance coefficient of this structure. With allother factors being the same, a wider structure may have a smaller axialcompliance coefficient than a similar but narrower structure. For a setincluding one or more structure, a combined average width of allstructures in the set may be used as one of many indicators of the axialcompliance coefficient of this set. However, this is not the onlyindicators. As such, even with first structures 120 a and secondstructures 120 b having the same combined average width, the first axialcompliance coefficient of first set 117 may be greater than the secondaxial compliance coefficient of second set 119 of second structures 120b.

For purposes of this disclosure, an individual average width of a singlestructure is defined as a ratio of the cross-sectional area (or half ofthe cross-sectional area for annular structures) to the length of thisstructure. The length is defined as its dimension in a directionperpendicular to longitudinal central axis 112. This definition accountsfor non-rectangular shapes of structures, such as structures havingtaper, shaped structure, and the like. Unless specifically, noted awidth of structure is referred to as an average width of this structure.The combined average width of a set is defined as a sum of individualaverage widths of all structures in this set. These individual averagewidths within the same set may all the same or different (e.g., increasefrom one end of the set to the other end).

When first structures 120 a and second structures 120 b have identicalcombined average widths, first structures 120 a and second structures120 b may have identical individual widths. Furthermore, identicalcombined average widths in two different sets may be achieved usingstructures having different individual widths. In one example, all firststructures 120 a may have identical individual widths. In the sameexample, all second structures 120 b may have identical individualwidths, which may be the same as the individual widths of firststructures 120 a. In this case, the number of first structures 120 a andsecond structures 120 b may be the same (in order for the combinedaverage widths to be the same for both sets). Furthermore, in this case,the difference between axial compliance coefficients of the two sets maybe attributed to different factors. Alternatively, all second structures120 b may have identical individual widths, but these individual widthsmay be different from individual widths of first structures 120 a. Inthis case, the number of first structures 120 a is different from thenumber of second structures 120 b (in order for the combined averagewidths to be the same for both sets). This difference in individualwidths and/or number of structures between first set 117 and second set119 may result in axial compliance coefficients of these two sets beingdifferent.

Furthermore, the individual widths of structures within each set maydiffer. For example, at least one of first structures 120 a may have adifferent individual width that at least another one of first structure120 a. In this example, all second structures 120 b may have identicalindividual widths. Alternatively, at least one of second structures 120b may have a different individual width that at least another one ofsecond structure 120 b. In another example, at least one of secondstructures 120 b may have a different individual width that at leastanother one of second structure 120 b. In this example, all firststructures 120 a may have the same individual width. Alternatively, atleast one of first structures 120 a may have a different individualwidth that at least another one of first structure 120 a.

Referring generally to FIGS. 7A, 8A-8B, and 9A-9B, and particularly to,e.g., FIG. 7A, first structures 120 a have a first combined averagewidth measured along longitudinal central axis 112 of shank 110. Secondstructures 120 b have a second combined average width measured alonglongitudinal central axis 112 of shank 110. The first combined averagewidth is different from the second combined average width. The precedingsubject matter of this paragraph characterizes example 47 of the presentdisclosure, wherein example 47 includes the subject matter of any one ofexamples 38-45, above. Different combined average widths of firststructures 120 a in first set 117 and second structures 120 b om secondset 119 may yield different axial compliance coefficients in these sets.FIG. 7A illustrates shank 110 that has first structure 120 a and secondstructure 120 b. Individual width W₁ of first structure 120 a is smallerthan individual width W₂ of second structure 120 b. As a result, firststructure 120 a may have a larger axial compliance coefficient thansecond structure 120 b. Scaling up this example to sets, the firstcombined average width of first structures 120 a is different from thesecond combined average width of second structures 120 b resulting inthe first axial compliance coefficient of first set 117 being differentfrom the second axial compliance coefficient of second set 119.

While the first combined average width is different from the secondcombined average width, individual widths of all structures in each setmay be the same or different. For example, the individual widths of allfirst structures 120 a may be the same. In this example, the individualwidths of all second structures 120 b may be the same but different fromthe individual widths of first structures 120 a. For example, theindividual widths of all second structures 120 b may greater than theindividual widths of first structures 120 a. Alternatively, theindividual widths of all second structures 120 b may be the same andalso the same as the individual widths of first structures 120 a.However, the number of first structures 120 a may be different from thenumber of second structures 120 b. For example, the number of secondstructures 120 b may greater than the number of first structures 120 a.In alternative examples, the individual widths of second structures 120b may different. Furthermore, the individual widths of all secondstructures 120 b may the same, but the individual widths of firststructures 120 a may different. For example, at least one of firststructures 120 a may have a different individual width that at leastanother one of first structure 120 a.

Referring generally to FIGS. 7A, 8A-8B, and 9A-9B, and particularly to,e.g., FIG. 7A, the first combined average width is less than the secondcombined average width. The preceding subject matter of this paragraphcharacterizes example 48 of the present disclosure, wherein example 48includes the subject matter of example 47, above. As noted above,different widths of the structures in first set 117 and second set 119may yield different axial compliance coefficients in these sets. Since agreater combined average width may result in a lower axial compliancecoefficient, the first combined average width may be less than thesecond combined average width in order for the first axial compliancecoefficient of first set 117 to be greater than the second axialcompliance coefficient of second set 119.

In some examples, the first combined average width is less than thesecond combined average width by at least about 5% or even at leastabout 50% or even 100%. The first combined average width may be lessthan the second combined average width due one or more factors, such asdifferent average individual widths of first structures 120 a and secondstructures 120 b, different number of first structures 120 a and secondstructures 120 b, or a combination of both. Furthermore, as describedabove, individual widths of all structures in each set may be the sameor different.

Referring generally to FIGS. 8A-8B, and 9A-9B, and particularly to,e.g., FIG. 7C, first structures 120 a have a first combined lengthmeasured perpendicular to longitudinal central axis 112 of shank 110.Second structures 120 b have a second combined length measuredperpendicular to longitudinal central axis 112 of shank 110. The firstcombined length is identical to the second combined length. Thepreceding subject matter of this paragraph characterizes example 49 ofthe present disclosure, wherein example 49 includes the subject matterof any one of examples 38-47, above.

A length of a structure is one of factors determining the axialcompliance coefficient of this structure. With all other factors beingthe same, a longer structure may have a larger axial compliancecoefficient than a similar, but shorter structure. For a set includingone or more structures, a combined length of all structures in the setis one of several factors affecting the axial compliance coefficient ofthe set. As noted above, the combined average width of the structures ineach set may be another factor affecting the axial compliancecoefficient. Accordingly, even with first structures 120 a and secondstructures 120 b having identical combined lengths, the first axialcompliance coefficient of first set 117 may be greater than the secondaxial compliance coefficient of second set 119 of second structures 120b. For example, first structures 120 a have a smaller combined averagewidth than second structures 120 b as, for example, shown in FIG. 7C.

For purposes of this disclosure, an individual length of a structure isdefined as its dimension in a direction perpendicular to longitudinalcentral axis 112 measured from the base of the structure to the tip thestructure. FIG. 7A identifies length (L) of one structure. The base ofthe structure may be its connector. The tip of the structure may be apart of the surface engaging another component, e.g., a receiver, duringoperation of shank 110. The combined length of a set is defined as a sumof individual lengths of all structures in this set. All structureswithin the same set have identical individual lengths. Furthermore,first structures 120 a and second structures 120 b have identicalindividual lengths. In other words, all structures of shank 110 haveidentical individual lengths. When the number of first structures 120 ais identical to the number of second structures 120 b, the firstcombined length is identical to the second combined length. In thiscase, the difference between axial compliance coefficients of the twosets may be attributed to other factors (e.g., different combinedaverage widths of first set 117 and second set 119).

Referring generally to FIGS. 8A-8B, and 9A-9B, and particularly to,e.g., FIG. 7D and 7E, first structures 120 a have a first combinedlength measured perpendicular to longitudinal central axis 112 of shank110. Second structures 120 b have a second combined length measuredperpendicular to longitudinal central axis 112 of shank 110. The firstcombined length is different from the second combined length. Thepreceding subject matter of this paragraph characterizes example 50 ofthe present disclosure, wherein example 50 includes the subject matterof any one of examples 38-47, above.

While the first combined length of first structures 120 a may bedifferent from the second combined length of second structures 120 b,individual lengths of all structures in both sets are identical.Accordingly, the number of first structures 120 a may be different fromthe number of second structures 120 b. For example, the number of secondstructures 120 b may be fewer than the number of first structures 120 a,as illustrated in FIG. 7E. In this example, individual widths of secondstructures 120 b are greater than individual widths of first structures120 a. It should be noted that in this example the first combinedaverage width may be the same as the second combined average width. Forexample, individual widths of second structures 120 b may be twicegreater than individual widths of first structures 120 a while there maybe twice fewer second structures 120 b than first structures 120 a.Alternatively, the number of second structures 120 b may be greater thanthe number of first structures 120 a, as illustrated in FIG. 7D.Individual widths of second structures 120 b may be the same asindividual widths of first structures 120 a as shown in FIG. 7D ordifferent. It should be noted that in both examples shown in FIGS. 7Dand 7E, the first axial compliance coefficient of first set 117 of firststructures 120 a is greater than the second axial compliance coefficientof second set 119 of the second structures 120 b.

Referring generally to FIGS. 8A-8B, and 9A-9B, and particularly to,e.g., FIG. 7E, the first combined length is greater than the secondcombined length. The preceding subject matter of this paragraphcharacterizes example 51 of the present disclosure, wherein example 51includes the subject matter of example 50, above.

As noted above, different combined lengths of first structures 120 a andsecond structures 120 b may yield different axial compliancecoefficients for their corresponding sets. Specifically, if the firstcombined length of first structures 120 a is greater than the secondcombined length of second structures 120 b, the first axial compliancecoefficient of first set 117 may be greater than the second axialcompliance coefficient of second set 119 as, for example, shown in FIG.7E.

In some examples, the first combined length is greater than the secondcombined length by at least about 5%. In other examples, the firstcombined length is greater than the second combined length by at leastabout 50%. In still other examples, the first combined length is greaterthan the second combined length by at least about 100%. When the firstcombined length is greater than the second combined length, this is dueto a larger number of first structures 120 a than of second structures120 b.

Referring generally to FIGS. 7A, 8A-8B, and 9A-9B, and particularly to,e.g., FIG. 7B, first structures 120 a have a first combined camberangle. Second structures 120 b have a second combined camber angle. Thefirst combined camber angle is identical to the second combined camberangle. The preceding subject matter of this paragraph characterizesexample 52 of the present disclosure, wherein example 52 includes thesubject matter of any one of examples 38-47, 49, or 50, above.

A camber angle of a structure is one of factors determining the axialcompliance coefficient of this structure. With all other factors beingthe same, a structure with a smaller camber angle may have a largeraxial compliance coefficient than a similar structure with a largercamber angle. For a set including one or more structures, a combinedcamber angle of all structures in the set may be used as one of manyindicators of the axial compliance coefficient of that set. As notedabove, the widths and lengths of structures in each set may otherindicators of the axial compliance coefficient of that set. As such,even with first structures 120 a and second structures 120 b havingidentical combined camber angles, the first axial compliance coefficientof first set 117 may be greater than the second axial compliancecoefficient of second set 119 of second structures 120 b.

For purposes of this disclosure, an individual camber angle of astructure (one of first structures 120 a or second structures 120 b) isdefined as an angle between one side of a cross-section of thatstructure and an axis extending perpendicular to longitudinal centralaxis 112 in the plane of the cross-section. When both sides of thecross-section of the structure are symmetrical with respect to thataxis, either one of the sides may be used for determining the individualcamber angle of this structure. However, when the two sides are notsymmetrical, an average value of camber angles of both sides is used asan individual camber angle for the corresponding structure. Theindividual camber angle may be positive or negative, depending on theposition of the side relative to the axis extending perpendicular tolongitudinal central axis 112. Another way of determining whether theindividual camber angle is positive or negative is based on the anglebetween the side and longitudinal central axis 112. Specifically, if theside and longitudinal central axis 112 form an obtuse angle, then theindividual camber angle is positive. However, if the side andlongitudinal central axis 112 form an acute angle, then the individualcamber angle is negative. Finally, if the side and longitudinal centralaxis 112 are perpendicular, then the individual camber angle is zero. Acombined camber angle of a set is defined as a sum of all individualcamber angles for all structures in that set.

When first structures 120 a and second structures 120 b have identicalcombined camber angles, first structures 120 a and second structures 120b may have identical individual camber angles. Furthermore, identicalcombined camber angles may be achieved in both sets with structureshaving different individual camber angles. In one example, all firststructures 120 a may have identical individual camber angles. In thesame example, all second structures 120 b may have identical individualcamber angles, which may be also identical to individual camber anglesof first structures 120 a. In this case, the number of first structures120 a and second structures 120 b may be identical. Furthermore, in thiscase, the difference between axial compliance coefficients of the twosets may be attributed to different factors (e.g., different combinedaverage widths of first set 117 and second set 119). Alternatively, allsecond structures 120 b may have identical individual camber angles, butthis camber angle may be different from the individual camber angle offirst structures 120 a (all first structures 120 a may have identicalindividual camber angles). In this case, the number of first structures120 a is different from the number of second structures 120 b. Thedifference in individual camber angles and numbers of the structures mayresult in different axial compliance coefficients of the two sets ofstructures.

Furthermore, individual camber angles of structures within each set maydiffer. For example, at least one of first structures 120 a may have adifferent individual camber angle that at least another one of firststructure 120 a. In this example, all second structures 120 b may haveidentical individual camber angles. Alternatively, at least one ofsecond structures 120 b may have a different individual camber anglethat at least another one of second structure 120 b. In another example,at least one of second structures 120 b may have a different individualcamber angle that at least another one of second structure 120 b. Inthis example, all first structures 120 a may have identical individualcamber angle. Alternatively, at least one of first structures 120 a mayhave a different individual camber angle that at least another one offirst structure 120 a.

Referring generally to FIGS. 7A, 8A-8B, and 9A-9B, and particularly to,e.g., FIG. 7B, first structures 120 a have a first combined camberangle. Second structures 120 b have a second combined camber angle. Thefirst combined camber angle is different from the second combined camberangle. The preceding subject matter of this paragraph characterizesexample 53 of the present disclosure, wherein example 53 includes thesubject matter of any one of examples 38-47, 49, or 50, above.

Different combined camber angles of first set 117 and second set 119 mayyield different axial compliance coefficients in these sets.

While the first combined camber angle is different from the secondcombined camber angle, individual camber angles of all structures ineach set may be identical or different. For example, individual camberangles of all first structures 120 a may be identical. In this example,the individual camber angles of all second structures 120 b may beidentical to each other, but different from the individual camber anglesof first structures 120 a. For example, the individual camber angles ofall second structures 120 b may be less than the individual camberangles of first structures 120 a. Alternatively, the individual camberangles of all second structures 120 b may be identical to each other andalso identical to the individual camber angles of first structures 120a. However, the number of first structures 120 a may be different fromthe number of second structures 120 b. For example, the number of secondstructures 120 b may greater than the number of first structures 120 a.In alternative examples, the individual camber angles of secondstructures 120 b may different. Furthermore, the individual camberangles of all second structures 120 b may identical, but the individualcamber angles of first structures 120 a may different. For example, atleast one of first structures 120 a may have a different individualcamber angle that at least another one of first structure 120 a.

Referring generally to FIGS. 7A, 8A-8B, and 9A-9B, and particularly to,e.g., FIG. 7B, the first combined camber angle is less than the secondcombined camber angle. The preceding subject matter of this paragraphcharacterizes example 54 of the present disclosure, wherein example 54includes the subject matter of example 53, above.

As noted above, different combined camber angles of first set 117 andsecond set 119 may yield different axial compliance coefficients inthese sets. Since a greater combined camber angle may result in a higheraxial compliance coefficient, the first combined camber angle may begreater than the second combined camber angle in order for the firstaxial compliance coefficient of first set 117 to be greater than thesecond axial compliance coefficient of second set 119.

In some examples, the first combined camber angle is greater than thesecond combined camber angle by at least about 5% or even at least about25% or even 50%. The first combined camber angle may be greater than thesecond combined camber angle due one or more factors, such as differentindividual camber angles of first structures 120 a and second structures120 b, different number of first structures 120 a and second structures120 b, or a combination of both. Furthermore, as described above, camberangles of all structures in each set may be the same or different.

Referring generally to FIGS. 1, 9A, and 9B, and particularly to, e.g.,FIG. 10, method 1000 further comprise arranging first set 117 of firststructures 120 a such that first set 117 of first structures 120 a has afirst axial compliance coefficient along longitudinal central axis 112of interior space 136. Method 1000 also comprises arranging second set119 of second structures 120 b such that second set 119 of secondstructures 120 b has a second axial compliance coefficient alonglongitudinal central axis 112 of interior space 136. The precedingsubject matter of this paragraph characterizes example 55 of the presentdisclosure, wherein example 55 includes the subject matter of any one ofexamples 38-54, above.

Referring generally to FIGS. 8A-8B, shank 110 further comprising cuttingedge 121. First structures 120 a are closer to cutting edge 121 thansecond structures 120 b. The preceding subject matter of this paragraphcharacterizes example 56 of the present disclosure, wherein example 56includes the subject matter of any one of examples 40-57, above. Cuttingedge 121 may be a drill bit, a countersink, a counter-bore, a tap, adie, a milling cutter, a reamer, or a cold saw blade. Additionalexamples of cutting edge 121 include, but are not limited to an endmill, a roughing end mill, a ball nose cutter, a slab mill, aside-and-face cutter, a involute gear cutter, a hob, a thread mill, aface mill, a fly cutter, a woodruff cutter, a hollow mill, a dovetailcutter, or a shell mill. When such examples of cutting edge 121 areused, an axial load may be applied to the structures as described above.

Examples of the present disclosure may be described in the context ofaircraft manufacturing and service method 1100 as shown in FIG. 11 andaircraft 1102 as shown in FIG. 12. During pre-production, illustrativemethod 1100 may include specification and design (block 1104) ofaircraft 1102 and material procurement (block 1106). During production,component and subassembly manufacturing (block 1108) and systemintegration (block 1110) of aircraft 1102 may take place. Thereafter,aircraft 1102 may go through certification and delivery (block 1112) tobe placed in service (block 1114). While in service, aircraft 1102 maybe scheduled for routine maintenance and service (block 1116). Routinemaintenance and service may include modification, reconfiguration,refurbishment, etc. of one or more systems of aircraft 1102.

Each of the processes of illustrative method 1100 may be performed orcarried out by a system integrator, a third party, and/or an operator(e.g., a customer). For the purposes of this description, a systemintegrator may include, without limitation, any number of aircraftmanufacturers and major-system subcontractors; a third party mayinclude, without limitation, any number of vendors, subcontractors, andsuppliers; and an operator may be an airline, leasing company, militaryentity, service organization, and so on.

As shown in FIG. 12, aircraft 1102 produced by illustrative method 1100may include airframe 1118 with a plurality of high-level systems 1120and interior 1122. Examples of high-level systems 1120 include one ormore of propulsion system 1124, electrical system 1126, hydraulic system1128, and environmental system 1130. Any number of other systems may beincluded. Although an aerospace example is shown, the principlesdisclosed herein may be applied to other industries, such as theautomotive industry. Accordingly, in addition to aircraft 1102, theprinciples disclosed herein may apply to other vehicles, e.g., landvehicles, marine vehicles, space vehicles, etc.

Apparatus(es) and method(s) shown or described herein may be employedduring any one or more of the stages of manufacturing and service method1100. For example, components or subassemblies corresponding tocomponent and subassembly manufacturing (block 1108) may be fabricatedor manufactured in a manner similar to components or subassembliesproduced while aircraft 1102 is in service (block 1114). Also, one ormore examples of the apparatus(es), method(s), or combination thereofmay be utilized during production stages 1108 and 1110, for example, bysubstantially expediting assembly of or reducing the cost of aircraft1102. Similarly, one or more examples of the apparatus or methodrealizations, or a combination thereof, may be utilized, for example andwithout limitation, while aircraft 1102 is in service (block 1114)and/or during maintenance and service (block 1116).

Different examples of the apparatus(es) and method(s) disclosed hereininclude a variety of components, features, and functionalities. Itshould be understood that the various examples of the apparatus(es) andmethod(s) disclosed herein may include any of the components, features,and functionalities of any of the other examples of the apparatus(es)and method(s) disclosed herein in any combination, and all of suchpossibilities are intended to be within the spirit and scope of thepresent disclosure.

Many modifications of examples set forth herein will come to mind to oneskilled in the art to which the present disclosure pertains having thebenefit of the teachings presented in the foregoing descriptions and theassociated drawings.

Therefore, it is to be understood that the present disclosure is not tobe limited to the specific examples illustrated and that modificationsand other examples are intended to be included within the scope of theappended claims. Moreover, although the foregoing description and theassociated drawings describe examples of the present disclosure in thecontext of certain illustrative combinations of elements and/orfunctions, it should be appreciated that different combinations ofelements and/or functions may be provided by alternative implementationswithout departing from the scope of the appended claims. Accordingly,parenthetical reference numerals in the appended claims are presentedfor illustrative purposes only and are not intended to limit the scopeof the claimed subject matter to the specific examples provided in thepresent disclosure.

1. A shank (110) comprising: a captive portion (116) comprising alongitudinal central axis (112), a captive end (118), a first set (117)of first structures (120 a), and a second set (119) of second structure(120 b), wherein: the first structures (120 a) extend away from thelongitudinal central axis (112) in a direction normal to thelongitudinal central axis (112); the second structures (120 b) extendaway from the longitudinal central axis (112) in a direction normal tothe longitudinal central axis (112); the first set (117) of the firststructures (120 a) and the second set (119) of the second structures(120 b) are each half as long along the longitudinal central axis (112)as the captive portion (116); the first set (117) of the firststructures (120 a) and the second set (119) of the second structures(120 b) do not overlap along the longitudinal central axis (112); thesecond set (119) of the second structures (120 b) is closer to thecaptive end (118) than the first set (117) of the first structures (120a); the first set (117) of the first structures (120 a) has a firstaxial compliance coefficient along the longitudinal central axis (112);the second set (119) of the second structures (120 b) has a second axialcompliance coefficient along the longitudinal central axis (112); andthe first axial compliance coefficient of the first set (117) of thefirst structures (120 a) is greater than the second axial compliancecoefficient of the second set (119) of the second structures (120 b). 2.The shank (110) of claim 1, wherein the first set (117) of the firststructures (120 a) and the second set (119) of the second structures(120 b) are indirectly connected together.
 3. The shank (110) of claim2, wherein: the first structures (120 a) are indirectly connectedtogether; and the second structures (120 b) are indirectly connectedtogether.
 4. The shank (110) of claim 1, wherein the first set (117) ofthe first structures (120 a) and the second set (119) of the secondstructures (120 b) are indirectly diffusion bonded together.
 5. Theshank (110) of claim 4, wherein: the first structures (120 a) areindirectly diffusion bonded together; and the second structures (120 b)are indirectly diffusion bonded together.
 6. The shank (110) of claim 1,wherein: at least one of the first structures (120 a) is made of a firstmaterial; at least one of the second structures (120 b) is made of asecond material; and the first material is identical to the secondmaterial.
 7. The shank (110) of claim 6, wherein: at least another oneof the first structures (120 a) is made of a third material; at leastanother one of the second structures (120 b) is made of a fourthmaterial; the first material is different from the third material; andthe second material is different from the fourth material.
 8. The shank(110) of claim 1, wherein: at least one of the first structures (120 a)is made of a first material; at least one of the second structures (120b) is made of a second material; and the first material is differentfrom the second material.
 9. The shank (110) of claim 8, wherein: atleast another one of the first structures (120 a) is made of a thirdmaterial; at least another one of the second structures (120 b) is madeof a fourth material; the first material is identical to the thirdmaterial; and the second material is identical to the fourth material.10. The shank (110) of claim 1, wherein: the first structures (120 a)have a first combined average width measured along the longitudinalcentral axis (112) of the shank (110); the second structures (120 b)have a second combined average width measured along the longitudinalcentral axis (112) of the shank (110); and the first combined averagewidth is identical to the second combined average width.
 11. The shank(110) of claim 1, wherein: the first structures (120 a) have a firstcombined average width measured along the longitudinal central axis(112) of the shank (110); the second structures (120 b) have a secondcombined average width measured along the longitudinal central axis(112) of the shank (110); and the first combined average width isdifferent from the second combined average width.
 12. (canceled)
 13. Theshank (110) of claim 1, wherein: the first structures (120 a) have afirst combined length measured perpendicular to the longitudinal centralaxis (112) of the shank (110); the second structures (120 b) have asecond combined length measured perpendicular to the longitudinalcentral axis (112) of the shank (110); and the first combined length isidentical to the second combined length.
 14. The shank (110) of claim 1,wherein: the first structures (120 a) have a first combined lengthmeasured perpendicular to the longitudinal central axis (112) of theshank (110); the second structures (120 b) have a second combined lengthmeasured perpendicular to the longitudinal central axis (112) of theshank (110); and the first combined length is different from the secondcombined length.
 15. (canceled)
 16. The shank (110) of claim 1, wherein:the first structures (120 a) have a first combined camber angle; thesecond structures (120 b) have a second combined camber angle; and thefirst combined camber angle is identical to the second combined camberangle.
 17. The shank (110) of claim 1, wherein: the first structures(120 a) have a first combined camber angle; the second structures (120b) have a second combined camber angle; and the first combined camberangle is different from the second combined camber angle. 18-19.(canceled)
 20. A shank (110) comprising: a captive portion (116)comprising a longitudinal central axis (112), a captive end (118), afirst set (117) of first structures (120 a), and a second set (119) ofsecond structures (120 b), wherein: the first structures (120 a) extendaway from the longitudinal central axis (112) in a direction normal tothe longitudinal central axis (112); the second structures (120 b)extend away from the longitudinal central axis (112) in a directionnormal to the longitudinal central axis (112); and the first set (117)of the first structures (120 a) and the second set (119) of the secondstructures (120 b) are indirectly connected together. 21-37. (canceled)38. A method of forming a shank (110), the method comprising: arrangingfirst structures (120 a) in a first set (117) of the first structures(120 a) and second structures (120 b) in a second set (119) of thesecond structures (120 b) such that the first structures (120 a) and thesecond structures (120 b) extend away from a longitudinal central axis(112) in a direction normal to the longitudinal central axis (112); andindirectly bonding the first set (117) of the first structures (120 a)to the second set (119) of the second structures (120 b).
 39. The methodof claim 38, further comprising indirectly bonding the first structures(120 a) together and indirectly bonding the second structures (120 b)together.
 40. The method of claim 39, wherein: indirectly bonding thefirst structures (120 a) together comprises indirectly diffusion bondingthe first structures (120 a) together, and indirectly bonding the secondstructures (120 b) together comprises indirectly diffusion bonding thesecond structures(120 b) together.
 41. The method of claim 38, whereinindirectly bonding the first set (117) of the first structures (120 a)to the second set (119) of the second structures (120 b) comprisesindirectly diffusion bonding the first set (117) of the first structures(120 a) to the second set (119) of the second structures (120 b). 42-56.(canceled)